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Dividing powers with negative exponents

How to divide exponents with negative exponents?

See the following examples.

Examples of dividing exponents with negative exponents

Example 1.

Dividing powers with the same base and negative exponents

5-45 ÷ 5-43 =
5-45 - (-43) =
5-2 =
1/52 = 1/25

See Powers of 5.

Example 2.

Dividing exponents with unequal bases and negative powers

4-3 ÷ 6-3 =
(4 ÷ 6)-3 =
(2 ÷ 3)-3 =
1/(2/3)3 =
1/(8/27) =
27/8 = 3,375

See Powers of 3.

Example 3.

Simplifying exponents with negative exponents

20-7 ÷ 10-7 =
(20 ÷ 10)-7 =
2-7 =
1/27 = 1/128

See Powers of 2.

Example 4.

Dividing exponents with negative exponents

21-10 ÷ 7-5 =
(3 * 7)-10 ÷ 7-5 =
(3-10 * 7-10 ): 7-5 =
3-10 * (7-10 ÷ 7-5) =
3-10 * (7-10 - (-5)) =
3-10 * (7-5) =
(32)-5 * 7-5 =
(32 * 7)-5 =
(9 * 7)-5 =
63-5 =
1/635