McGraw Hill Math Grade 7 Lesson 16.1 Answer Key Exponents

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McGraw-Hill Math Grade 7 Answer Key Lesson 16.1 Exponents

Exercises

CALCULATE

Question 1.
122 = _____________
Answer:
122 = 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.
104 = _____________
Answer:
104 = 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.
73 = _____________
Answer:
73 = 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.
23 = _____________
Answer:
23 = 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.
44 = _____________
Answer:
44 = 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.
53 = _____________
Answer:
53 = 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.
412 = _____________
Answer:
412 = 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.
55 = _____________
Answer:
55 = 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.
67 = _____________
Answer:
67 = 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.
174 = _____________
Answer:
174 = 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.
010 = _____________
Answer:
010 = 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.
1010 = _____________
Answer:
1010 = 1
A base raised to the zero power is equal to 1. So, 1010 is equal to 1.

Question 13.
121 = _____________
Answer:
121 = 12
A base raised to the first power is equal to the base. So, 121 is equal to 12.

Question 14.
240 = _____________
Answer:
240 = 1
A base raised to the zero power is equal to 1. So, 240 is equal to 1.

Question 15.
331 = _____________
Answer:
331 = 33
A base raised to the first power is equal to the base. So, 331 is equal to 33.

MULTIPLY OR DIVIDE

Question 1.
23 ÷ 2-5 = _____________
Answer:
23 ÷ 2-5 = 2(3 – (-5))  = 28 
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 28.

Question 2.
55 × 5-6 = _____________
Answer:
55 × 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.
1111 ÷ 114 = _____________
Answer:
1111 ÷ 114 = 11(11 – 4)  = 117 
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 117.

Question 4.
544 ÷ 54-2 = _____________
Answer:
544 ÷ 54-2 = 54(4 – (-2)) = 54(4 + 2)= 546 
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 546.

Question 5.
32 ÷ 30 = _____________
Answer:
32 ÷ 30 = 3(2 – 0) = 32 
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 32.

Question 6.
81 × 88 = _____________
Answer:
81 × 88 = 8(1 + 8)  = 89    
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 89.

Question 7.
155 ÷ 154 = _____________
Answer:
155 ÷ 154 = 15(5 – 4) = 151 
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.
86 ÷ 82 = _____________
Answer:
86 ÷ 82 = 8(6 – 2) = 84 
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 84.

Question 9.
187 × 1821 = _____________
Answer:
187 × 1821 = 18(7 + 21)  = 1828    
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 1828.

Question 10.
8110 ÷ 817 = _____________
Answer:
8110 ÷ 817 = 81(10 – 7) = 813 
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 813.

Question 11.
1919 × 1916 = _____________
Answer:
1919 × 1916 = 19(19 + 16)  = 1935    
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 1935.

Question 12.
212 ÷ 213 = _____________
Answer:
212 ÷ 213 = 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 ÷ 156 = _____________
Answer:
15-5 ÷ 156 = 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)= 104 
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.
1715 ÷ 1722 = _____________
Answer:
1715 ÷ 1722 = 17(15 – 22) = 17-7 = 1/177
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.

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