Excel in your academics by accessing **McGraw Hill Math Grade 7 Answer Key PDF Lesson 16.1 Exponents **existing for free of cost.

## McGraw-Hill Math Grade 7 Answer Key Lesson 16.1 Exponents

**Exercises**

**CALCULATE**

Question 1.

12^{2} = _____________

Answer:

12^{2 }= 12 x 12 = **144
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 12 and exponent is 2. So, we have to multiply the base 12 by itself as two times the product is equal to 144.

Question 2.

10^{4} = _____________

Answer:

10^{4 }= 10 x 10 x 10 x 10 = **10,000
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 10 and exponent is 4. So, we have to multiply the base 10 by itself as four times the product is equal to 10,000.

Question 3.

7^{3} = _____________

Answer:

7^{3 }= 7 x 7 x 7 = **343
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 7 and exponent is 3. So, we have to multiply the base 7 by itself as three times the product is equal to 343.

Question 4.

2^{3} = _____________

Answer:

2^{3 }= 2 x 2 x 2 = **8
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 2 and exponent is 3. So, we have to multiply the base 2 by itself as three times the product is equal to 8.

Question 5.

4^{4} = _____________

Answer:

4^{4 }= 4 x 4 x 4 x 4 = **256
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 4 and exponent is 4. So, we have to multiply the base 4 by itself as four times the product is equal to 256.

Question 6.

5^{3} = _____________

Answer:

5^{3 }= 5 x 5 x 5 = **125
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 5 and exponent is 3. So, we have to multiply the base 5 by itself as three times the product is equal to 125.

Question 7.

41^{2} = _____________

Answer:

41^{2 }= 41 x 41= **1,681
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 41 and exponent is 2. So, we have to multiply the base 41 by itself as two times the product is equal to 1,681.

Question 8.

5^{5} = _____________

Answer:

5^{5 }= 5 x 5 x 5 x 5 = **3,125
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 5 and exponent is 5. So, we have to multiply the base 5 by itself as five times the product is equal to 3,125.

Question 9.

6^{7} = _____________

Answer:

6^{7 }= 6 x 6 x 6 x 6 x 6 x 6 x 6 = **279,936
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 6 and exponent is 7. So, we have to multiply the base 6 by itself as seven times the product is equal to 279,936.

Question 10.

17^{4} = _____________

Answer:

17^{4 }= 17 x 17 x 17 x 17 = **83,521
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 17 and exponent is 4. So, we have to multiply the base 17 by itself as four times the product is equal to 83,521.

Question 11.

0^{10} = _____________

Answer:

0^{10 }= **0
**Explanation:

The exponent number tells how many times we have to multiply the base by itself. Here base is 0 and exponent is 10. So, we have to multiply the base 0 by itself as ten times the product is equal to 0.

Question 12.

101^{0} = _____________

Answer:

101^{0} = **1**

A base raised to the zero power is equal to 1. So, 101^{0} is equal to 1.

Question 13.

12^{1} = _____________

Answer:

12^{1} = **12**

A base raised to the first power is equal to the base. So, 12^{1} is equal to 12.

Question 14.

24^{0} = _____________

Answer:

24^{0} = **1**

A base raised to the zero power is equal to 1. So, 24^{0} is equal to 1.

Question 15.

33^{1} = _____________

Answer:

33^{1} = **33**

A base raised to the first power is equal to the base. So, 33^{1} is equal to 33.

**MULTIPLY OR DIVIDE**

Question 1.

2^{3} ÷ 2^{-5} = _____________

Answer:

2^{3} ÷ 2^{-5} = 2^{(3 – (-5)) } =** 2 ^{8} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 2

^{8}.

Question 2.

5^{5} × 5^{-6} = _____________

Answer:

5^{5} × 5^{-6} = 5^{(5 + (-6)) } = **5 ^{-1 }**=

**1/5**

^{ }Explanation:

If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 5

^{-1}.

Question 3.

11^{11} ÷ 11^{4} = _____________

Answer:

11^{11} ÷ 11^{4} = 11^{(11 – 4) } =** 11 ^{7} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 11

^{7}.

Question 4.

54^{4} ÷ 54^{-2} = _____________

Answer:

54^{4} ÷ 54^{-2} = 54^{(4 – (-2))} = 54^{(4 + 2)}=** 54 ^{6} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 54

^{6}.

Question 5.

3^{2} ÷ 3^{0} = _____________

Answer:

3^{2} ÷ 3^{0} = 3^{(2 – 0)} =** 3 ^{2} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 3

^{2}.

Question 6.

8^{1} × 8^{8} = _____________

Answer:

8^{1} × 8^{8 }= 8^{(1 + 8) } = **8 ^{9 }**

^{ }Explanation:

If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 8

^{9}.

Question 7.

15^{5} ÷ 15^{4} = _____________

Answer:

15^{5} ÷ 15^{4} = 15^{(5 – 4)} =** 15 ^{1} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 15.

Question 8.

8^{6} ÷ 8^{2} = _____________

Answer:

8^{6} ÷ 8^{2} = 8^{(6 – 2)} =** 8 ^{4} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 8

^{4}.

Question 9.

18^{7} × 18^{21} = _____________

Answer:

18^{7} × 18^{21} = 18^{(7 + 21) } = **18 ^{28 }**

^{ }Explanation:

If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 18

^{28}.

Question 10.

81^{10} ÷ 81^{7} = _____________

Answer:

81^{10} ÷ 81^{7} = 81^{(10 – 7)} =** 81 ^{3} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 81

^{3}.

Question 11.

19^{19} × 19^{16} = _____________

Answer:

19^{19} × 19^{16 }= 19^{(19 + 16) } = **19 ^{35 }**

^{ }Explanation:

If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 19

^{35}.

Question 12.

21^{2} ÷ 21^{3} = _____________

Answer:

21^{2} ÷ 21^{3} = 21^{(2 – 3)} =** 21 ^{-1 }= 1/21 **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 1/21.

Question 13.

15^{-5} ÷ 15^{6} = _____________

Answer:

15^{-5} ÷ 15^{6} = 15^{(-5 – 6)} =** 15 ^{-11} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 15

^{-11}.

Question 14.

10^{-8} ÷ 10^{-12} = _____________

Answer:

10^{-8} ÷ 10^{-12 }= 10^{(-8 – (-12))} =10^{(-8 + 12)}=** 10 ^{4} **

Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 10,000.

Question 15.

17^{15} ÷ 17^{22} = _____________

Answer:

17^{15} ÷ 17^{22} = 17^{(15 – 22)} = **17 ^{-7}**

**= 1/17**

^{7}Explanation:

If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 17

^{-7}.