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Dividing exponents with different powers

How do you divide exponents with different powers?

See the following examples.

Examples of dividing exponents with different powers

Example 1.

Divide exponents with different powers

2150 ÷ 2147 =
2150 - 147 =
23 = 8

See Powers of 2.

Example 2.

Simplifying exponents with different powers

32 ÷ 3(-2) =
322 - (-2) =
34 = 81

See Powers of 3.

Example 3.

Dividing exponents with different bases and powers

82 ÷ 26 =
(23)2 ÷ 26 =
23 * 2 ÷ 26 =
26 ÷ 26 = 1

See Powers of 2.

Example 4.

Dividing powers with the same base and unequal exponent

63 ÷ 66 =
63 - 6 =
6-3 =
1/63 = 1/216

See Powers of 6.

Example 5.

Dividing powers with the same base and different exponents

9-3 ÷ 9-2 =
9-3 - (-2) =
9-1 =
1/91 = 1/9