Exercises

CALCULATE

Question 1.
122 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
1010 = 1
A base raised to the zero power is equal to 1. So, 1010 is equal to 1.

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

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

Question 15.
331 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________
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 = _____________