Rules of Operation with Exponents

Question 1

1) Multiplying two powers with the same base, keep the base and add the exponents together.

2^2 x 2^3 = 2^(2+3) = 2^5

Answer 1

2) Dividing two powers with the same base, keep the base, and subtract the exponent of the denominator from the exponent of the numerator.

4^5 / 4^2 = 4^5-2 = 4^3

Question 2

3) To raise a power to another power, multiply the exponents.

(3^2)^4 = 3^(2x4) = 3^8

Answer 2

4) To multiply, two powers with different basis, but the same power, multiply the bases together and keep the same power.

(3^2) (5^2) = 15^2

Question 3

5) A base with a negative exponent indicates the reciprocal of that bass to the positive value of the exponent.

5^-3 = (1/5)^3 = 1/125

Answer 3

6) Raising any nonzero number to an exponent of zero equals 1.

5^0 = 1
(-6)^0 = 1
161^0 = 1

Question 4

Raising an even number to any positive integer exponent gives an even number.
8^5 = 32,768 (even)

Raising an odd number to any integer exponent greater than or equal to zero gives an odd number.
5^8 = 390, 625 (odd)