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#Multiplying exponents - How to multiply exponents

How to multiply exponents.

Multiplying exponents with same base

For exponents with the same base, we should add the exponents:

a n · a m = a n+m

Example:

2 3 · 2 4 = 2 3+4 = 2 7 = 2·2·2·2·2·2·2 = 128

Multiplying exponents with different bases

When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:

3 2 · 4 3 = 9 · 64 = 576

Multiplying negative exponents

a -n · a -m = a - ( n+m ) = 1 / a n+m

Example:

2 -3 · 2 -4 = 2 -(3+4) = 2 -7 = 1 / 2 7 = 1 / (2·2·2·2·2·2·2) = 1 / 128 = 0.0078125

When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:

Multiplying fractions with exponents

Multiplying fractional exponents

Multiplying square roots with exponents