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Rules for powers with positive integer exponents

Rules for powers with positive integer exponents.

Here a and b are real numbers, a ≠ 0, b ≠ 0; m and n are integers.

Multiplying powers of the same base

Multiplying powers of the same base:

aman = am + n

Here we add exponents.

Multiplying powers of different bases

Multiplication of powers with different base but same exponents:

ambm = (ab)m

Multiplication of powers with different bases but same exponents is equal to a power of the product of the bases.

Power raised to a power

If there is a power raised to a power, multiply the exponents:

(am)n = am * n

Dividing powers with the same base

Dividing powers with the same base:

am : an = am - n

Dividing powers with different bases

Division of powers with different bases but same exponents:

an : bn = (a/b)n