SBP-Program

f

tw

in

Adding powers with the same base and exponents

How do you add powers with the same base and exponents?

See the following examples.

Examples of adding powers with the same base and exponents

1. Adding two powers with the same base

25 + 25 =
25(1 + 1) =
2 * 25 =
21 * 25 =
21 + 5 =
26 = 64

Or shorter

25 + 25 =
2 * 25 =
2 * 32 = 64

See Powers of 2.

2. Adding exponential expressions with the same base

83 + 83 =
2 * 83 =
2 * (23)3 =
21 * 23 * 3 =
21 * 29 =
21 + 9 =
210 = 1024

Or shorter

83 + 83 =
(8 + 8)(82 - 8 * 8 + 82) =
16 * 64 = 1024

See Powers of 8.

3. Adding powers with the same base and exponents

(-6)5 + (-6)5 =
2 * (-6)5 =
2 * (-7776) =
-15552

The result is negative.

See Powers of 6.

4. Adding powers with the same base and exponents

(-6)4 + (-6)4 =
2 * (-6)4 =
2 * 1296 = 2592

The result is positive.

See Powers of 6.