Spectrum Math Grade 6 Chapter 5 Lesson 1 Answer Key Using Exponents (2024)

Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.1 Using Exponentsand get the proper assistance needed during your homework.

Spectrum Math Grade 6 Chapter 5 Lesson 5.1 Using Exponents Answers Key

A power of a number represents repeated multiplication of the number by itself.
10³ = 10 × 10 × 10 and is read 10 to the third power.
In exponential numbers, the base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In 2⁵, 2 is the base and 5 is the exponent.
2⁵ means 2 is used as a factor 5 times.
2 × 2 × 2 × 2 × 2 = 32 2⁵ = 32
Scientific notation for a number is expressed by writing the number as the product of a number between one and ten, and a power of ten.
3,000 can be written as 3 × 1,000 or 3 × 10³.
3 × 10³ is scientific notation for 3,000.
Some powers of 10 are shown in the table at right.

Use the table above to write each number in scientific notation.

Question 1.
a. 30 ______
Answer:
The given number in Scientific notation can be written as 3 x 10¹

b. 4,000 ______
Answer:
The given number in Scientific notation can be written as 4 x 10³

c. 50,000 _____
Answer:
The given number in Scientific notation can be written as5 x 10⁴

Question 2.
a. 600,000 ____
Answer:
The given number in Scientific notation can be written as 6 x 10⁵

b. 700 ____
Answer:
The given number in Scientific notation can be written as 7 x 10²

c. 90 _____
Answer:
The given number in Scientific notation can be written as 9 x 10¹

Question 3.
a. 40,000 ____
Answer:
The given number in Scientific notation can be written as 4 x 10⁴

b. 100,000 ____
Answer:
The given number in Scientific notation can be written as 1 x 10⁵

c. 400 ____
Answer:
The given number in Scientific notation can be written as 4 x 10²

Write each power as the product of factors.

Question 4.
a. 3³ ______
Answer:
Given value is 3³
It can be written as a product of 3 x 3 x 3
= 27
Therefore the value of 3³ is27.

b. 5⁵ ______
Answer:
Given value is 5⁵
It can be written as a product of 5 x 5 x 5
=125
Therefore the value of 5⁵is 125 .

c. 1⁶ ______
Answer:
Given value is 1⁶
It can be written as a product of 1 x 1 x 1 x 1 x 1 x 1
=1
Therefore the value of 1⁶ is 1.

Question 5.
a. 12² ______
Answer:
Given value is 12²
It can be written as a product of 12 x 12
=144
Therefore the value of 12² is 144.

b. 8³ ______
Answer:
Given value is 8³
It can be written as a product of 8 x 8 x 8
=512
Therefore the value of 8³ is 512 .

c. 6³ ______
Answer:
Given value is 6³
It can be written as a product of 6 x 6 x 6
=216
Therefore the value of 6³ is 216 .

Question 6.
a. 7⁴ ______
Answer:
Given value is 7⁴
It can be written as a product of 7 x 7 x 7 x 7
=2401
Therefore the value of 7⁴ is 2401.

b. 4⁴ ______
Answer:
Given value is 4⁴
It can be written as a product of 4 x 4 x 4 x 4
= 256
Therefore the value of 4⁴ is 256 .

c. 11⁴ ______
Answer:
Given value is 11⁴
It can be written as a product of 11 x 11 x 11 x 11
= 14641
Therefore the value of 11⁴ is 14641.

Use exponents to rewrite each expression.

Question 7.
a. 3 × 3 × 3 ____
Answer:
Given 3 x 3 x 3
It can be written as a 3³
= 27
Therefore the value of 3 x 3 x 3 is 3³ which is equal to 27.

b. 8 × 8 _____
Answer:
Given 8 x 8
It can be written as 8²
= 64
Therefore the value of 8x 8 is 8² which is equal to 64.

c. 7 × 7 × 7 × 7 × 7 _____
Answer:
Given 7 × 7 × 7 × 7 × 7
It can be written as 7⁵
= 16,807
Therefore the value of 7 × 7 × 7 × 7 × 7 is 7⁵ which is equal to 16,807.

Question 8.
a. 24 × 24 _____
Answer:
Given 24 × 24
It can be written as 24²
= 576
Therefore the value of 24 × 24 is 24² which is equal to 576.

b. 4 × 4 × 4 _____
Answer:
Given 4 × 4 x 4
It can be written as 4³
= 64
Therefore the value of 24 × 24 is 4³which is equal to 64.

c. 6 × 6 × 6 × 6 × 6 × 6 _____
Answer:
Given 6 × 6 × 6 × 6 × 6 × 6
It can be written as 6⁶
=46,656
Therefore the value of 6 × 6 × 6 × 6 × 6 × 6 is 6⁶ which is equal to 46,656 .

Question 9.
a. 2 × 2 × 2 × 2 ____
Answer:
Given 2 × 2 × 2 × 2
It can be written as 2⁴
= 16
Therefore the value of 2 × 2 × 2 × 2 is 2⁴ which is equal to 16.

b. 38 × 38 × 38 _____
Answer:
Given 38 × 38 × 38
It can be written as 38³
= 54,872
Therefore the value of 38 x 38 x38 is 38³ which is equal to 54,872.

c. 5 × 5 × 5 × 5 × 5 _____
Answer:
Given 5 × 5 × 5 × 5 × 5
It can be written as 5⁵
= 3125
Therefore the value of 5 x 5 x 5 x 5 x 5 is 5⁵ which is equal to 3125.

Question 10.
a. a⁴ if a = 2 ____
Answer:
Given Expression a⁴
By Substituting the given value a = 2, the Expression becomes as shown Below
a⁴ = 1⁴
= 1 x 1 x 1 x 1
= 1
Therefore the value of a = 1

b. x³ if x = 4 ____
Answer:
Given Expression x³
By Substituting the given value x = 4, the Expression becomes as shown Below
x³ = 4³
= 4 x 4 x 4
= 64
Therefore the value of x is 64

c. n⁷ if n = 1 ____
Answer:
Given Expression n⁷
By Substituting the given value n = 1, the Expression becomes as shown Below
n⁷ = 1⁷
= 1 x 1 x1 x 1 x 1 x 1 x 1
= 1
Therefore the value of n is 1.

Question 11.
a. n² if n = 8 ____
Answer:
Given Expression n²
By Substituting the given value n =81, the Expression becomes as shown Below
n² = 8²
= 8 x 8
= 64
Therefore the value of n is 64.

b. b⁴ if b = 3 ____
Answer:
Given Expression b⁴
By Substituting the given value n =81, the Expression becomes as shown Below
^b4 = 3⁴
= 3 x 3 x 3 x 3
= 81
Therefore the value of b is 81.

c. x³ if x = 5 _____
Answer:
Given Expression x³
By Substituting the given value x =5, the Expression becomes as shown Below
^x3 = 5³
= 5 x 5 x 5
= 125
Therefore the value of x is 125.

Question 12.
a. a⁵ if a = 3 ____
Answer:
Given Expression a ⁵
By Substituting the given value a =3, the Expression becomes as shown Below
a ⁵ = 3⁵
= 3 x 3 x 3 x 3 x 3
= 243
Therefore the value of a is 243.

b. x³ if x = 6 ____
Answer:
Given Expression x³
By Substituting the given value x = 6, the Expression becomes as shown Below
x ³ = 6³
= 6 x 6 x 6
= 216
Therefore the value of x is 216.

c. n² if n = 11 ____
Answer:
Given Expression n²
By Substituting the given value n = 11 , the Expression becomes as shown Below
n² = 11²
= 11 x 11
= 121
Therefore the value of n is 121.

Write each power as the product of factors.

Question 1.
a.
3⁵ __________
Answer:
Given value is 3⁵
It can be written as a product of 3 x 3 x 3 x 3 x 3
=243
Therefore the value of 3⁵ is 243 .

b.
9³ __________
Answer:
Given value is 9³
It can be written as a product of 9 x 9 x 9
= 729
Therefore the value of 9³ is 729.

c.
2⁷ __________
Answer:
Given value is 2⁷
It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2
=128
Therefore the value of 2⁷ is 128 .

Question 2.
a.
10² __________
Answer:
Given value is 10²
It can be written as a product of 10 x 10
=100
Therefore the value of10²is 100 .

b.
3⁴ __________
Answer:
Given value is 3⁴
It can be written as a product of 3 x 3 x 3 x 3
= 81
Therefore the value of 3⁴ is 81.

c.
2⁸ __________
Answer:
Given value is 2⁸
It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
Therefore the value of 2⁸ is 256.

Question 3.
a.
7³ __________
Answer:
Given value is 7³
It can be written as a product of 7 x 7 x 7
= 343
Therefore the value of 7³ is 343 .

b.
4² __________
Answer:
Given value is 4²
It can be written as a product of 4 x 4
= 16
Therefore the value of 4² is 16 .

c.
7² __________
Answer:
Given value is 7²
It can be written as a product of 7 x 7
= 49
Therefore the value of 7² is 49.

Question 4.
a.
9³ __________
Answer:
Given value is 9³
It can be written as a product of 9 x 9 x 9
= 729
Therefore the value of 9³ is 729.

b.
8¹ __________
Answer:
Given value is 8¹
It can be written as a product of 8
= 8
Therefore the value of 8¹ is 8.

c.
12² __________
Answer:
Given value is 12²
It can be written as a product of 12 x 12
= 144
Therefore the value of 12² is 144.

Question 5.
a.
5⁴ __________
Answer:
Given value is 5⁴
It can be written as a product of 5 x 5 x 5 x 5
= 625
Therefore the value of 5⁴ is 625.

b.
11³ __________
Answer:
Given value is 11³
It can be written as a product of 11 x 11 x 11
= 1331
Therefore the value of 11³ is 1331.

c.
6⁵ __________
Answer:
Given value is 6⁵
It can be written as a product of 6 x 6 x 6 x 6 x 6
= 7,776
Therefore the value of 6⁵ is 7,776.

Question 6.
a.
4⁴ __________
Answer:
Given value is 4⁴
It can be written as a product of 4 x 4 x 4 x 4
= 256
Therefore the value of 4⁴ is 256.

b.
10³ __________
Answer:
Given value is 10³
It can be written as a product of 10 x 10 x 10
= 1000
Therefore the value of 10³ is 1000.

c.
8⁶ __________
Answer:
Given value is 8⁶
It can be written as a product of 8 x 8 x 8 x 8 x 8 x 8
= 2, 62,1 44
Therefore the value of 8⁶ is 2,62,144.

Use exponents to rewrite each expression.

Question 7.
a. 3 × 3 × 3 = ____
Answer:
Given Expression 3 × 3 × 3
It can be written as 3³
= 81
Therefore the value of 3 × 3 × 3 is 3³ which is equal to 81.

b. 5 × 5 × 5 × 5 × 5 = ____
Answer:
Given Expression 5 × 5 × 5 × 5 × 5
It can be written as 5⁵
=3125
Therefore the value of 5 × 5 × 5 × 5 × 5 is 5⁵ which is equal to 3125.

c. 2 × 2 × 2 × 2 × 2 × 2 = _____
Answer:
Given Expression 2 × 2 × 2 × 2 × 2 × 2
It can be written as2⁶
= 64
Therefore the value of 2 × 2 × 2 × 2 × 2 × 2 is2⁶ which is equal to 64.

Question 8.
a. 9 × 9 × 9 = ____
Answer:
Given Expression 9 × 9 × 9
It can be written as 9³
= 729
Therefore the value of 9 × 9 × 9 is 9³ which is equal to 729.

b. 4 × 4 × 4 × 4 × 4 × 4 × 4 = ____
Answer:
Given Expression 4 × 4 × 4 × 4 × 4 × 4 × 4
It can be written as4⁷
=16384
Therefore the value of 4 × 4 × 4 × 4 × 4 × 4 × 4 is4⁷ which is equal to 16384.

c. 21 × 21 = ____
Answer:
Given Expression 21 x 21
It can be written as21²
= 441
Therefore the value of 21 x 21 is21² which is equal to 441.

Question 9.
a. 10 × 10 × 10 × 10 = ____
Answer:
Given Expression 10 x 10 x 10 x 10
It can be written as 10⁴
= 10,000
Therefore the value of 10 x 10 x 10 x 10 is 10⁴ which is equal to 10,000.

b. 8 × 8 × 8 × 8 × 8 = ____
Answer:
Given Expression 8 × 8 × 8 × 8 × 8
It can be written as 8⁵
= 32,768
Therefore the value of 8 × 8 × 8 × 8 × 8 is 8⁵ which is equal to 32,768.

c. 7 × 7 × 7 × 7 = ____
Answer:
Given Expression 7 × 7 × 7 × 7
It can be written as 7⁴
= 2,401
Therefore the value of 7 × 7 × 7 × 7 is 7⁴which is equal to 2401.

Evaluate each expression.

Question 10.
a. 8⁵ _____
Answer:
Given value is 8⁵
It can be written as a product of 8 x 8 x 8 x 8 x 8
= 32,768
Therefore the value of 8⁵ is Equal to 32,768.

b. 2⁸ _____
Answer:
Given value is 2⁸
It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
Therefore the value of 2⁸ is Equal to 256.

c. 3⁴ _____
Answer:
Given value is 3⁴
It can be written as a product of 3 x 3 x 3 x 3
= 81
Therefore the value of 3⁴ is Equal to 81.

Question 11.
a. 6² _____
Answer:
Given value is 6²
It can be written as a product of 6 x 6
= 36
Therefore the value of 6² is Equal to 36.

b. 9¹ _____
Answer:
Given value is 9¹
It can be written as a product of 9
= 9
Therefore the value of 9¹ is Equal to 9.

c. 10⁴ _____
Answer:
Given value is 10⁴
It can be written as a product of 10 x 10 x 10 x 10
= 10, 000
Therefore the value of 10⁴ is Equal to 10,000.

Question 12.
a. 4⁴ _____
Answer:
Given value is 4⁴
It can be written as a product of 4 x 4 x 4 x 4
= 256
Therefore the value of 4⁴ is Equal to 256.

b. 7⁴ _____
Answer:
Given value is 7⁴
It can be written as a product of 7 x 7 x 7 x 7
= 2401
Therefore the value of 7⁴ is Equal to 2401.

c. 12² _____
Answer:
Given value is 12²
It can be written as a product of 12 x 12
= 144
Therefore the value of 12² is Equal to 144 .