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Dividing powers with the same base

How do you divide exponents with the same base?

See the following examples.

Examples of dividing exponents with the same base

Example 1.

Dividing exponents with the same base

45 = 
42
45 - 2 =
43 = 64

See Powers of 4.

Example 2.

Dividing 2 exponents with the same base

(25a)55 = 
(25a)53
(25a)55 - 53 =
(25a)2 =
252a2 = 625a2

Example 3.

Dividing powers with the same base and negative exponents

77 = 
79
77 - 9 =
7-2 = 
1 = 1
7249

See Powers of 7.

Example 4.

Dividing 3 exponents with the same base

99 ÷ 95 ÷ 92 =
(99 ÷ 95) ÷ 92 =
(99 - 5) ÷ 92 =
94 ÷ 92 =
94 - 2 =
92 = 81

Or shorter

99 ÷ 95 ÷ 92 =
99 - 5 - 2 =
92 = 81

See Powers of 9.