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Subtracting powers with different bases

How to subtract powers with different bases?

See the following examples.

Examples of subtracting powers with different bases

1. Subtracting powers with different bases and equal exponents

68 - 38 =
(2 * 3)8 - 38 =
28 * 38 - 38 =
38(28 - 1) =
6561(256 - 1) = 1673055

See Powers of 3.

2. Subtraction of powers with unequal bases and same exponent

92 - 122 =
(3 * 3)2 - (3 * 4)2 =
32 * 32 - (32 * 42) =
32(32 - 42) =
9(9 - 16) = −63

See Powers of 4.

3. Subtract powers with different bases and same exponent

206 - 106 =
(2 * 10)6 - 106 =
(26 * 106) - 106 =
106(26 - 1) =
1000000(64 - 1) = 63000000

See Powers of 10.

4. Subtracting powers with different bases and different exponents

(2a)4b - ab =
(24b * a4b) - ab =
(24b * a3b + b) - ab =
(24b * a3b * ab) - ab =
ab((24b * a3b) - 1)