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Dividing exponents with the same base and different exponents

How do you divide exponents with the same base and different exponents?

See the following examples.

Examples of dividing exponents with the same base and different exponents

Example 1.

Dividing exponents with the same base and different exponents

810 ÷ 83 =
810 - 3 =
87 = 2097152

See Powers of 8.

Example 2.

Dividing powers with the same base and different exponents

98 ÷ (-9)5 =
(18 * 98) ÷ ((-1)5 * 95) =
(18 ÷ (-1)5) * (98 ÷ 95) =
(1 ÷ (-1)) * (98 - 5) =
-1 * 93 = - 729

See Powers of 9.

Example 3.

Dividing exponents with the same base and unequal negative exponents

6-15 ÷ 6-5 =
6-15 - (-5) =
6-15 + 5 =
6-10 =
1/610 = 1/60466176

See Powers of 6.

Example 4.

Dividing exponents with the same base and different exponents

23 ÷ 214 =
23 - 14 =
2-11 =
1/211 = 1/2048

See Powers of 2.