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Subtracting powers with different exponents

How to subtract powers with different exponents?

See the following examples.

Examples of subtracting powers with different exponents

1. Subtracting two powers with different exponents

56 - 52 =
52 + 4 - 52 =
52 * 54 - 52 =
52(54 - 1) =
25(625 - 1) = 15600

See Powers of 5.

2. Subtraction of powers with different exponents

72 - 73 =
72 - 71 + 2 =
72 - 71 * 72 =
72(1 - 71) =
49(1 - 7) = −294

See Powers of 7.

3. Subtracting powers with unequal exponents

96 - 93 =
92 * 3 - 93 =
(93)2 - 93 =
93(93 - 1) =
729(729 - 1) = 530712

See Powers of 9.

4. Subtraction of powers with dissimilar exponents

24a - 4a =
24 * a - (2 * 2)a =
(2a)4 - (2a * 2a) =
2a((2a)3 - 2a)