# Damia D. 2014. Bases and Exponents An exponent tells you how many times the base is multiplied by itself. x 4 = x ·x ·x ·x In this case, the larger number,

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Damia D. 2014

Bases and Exponents An exponent tells you how many times the base is multiplied by itself. x 4 = x ·x ·x ·x In this case, the larger number, the three, is the base and the smaller number, the seven, is the exponent. 3 7 = 3 · 3 · 3 · 3 · 3 · 3 · 3 So, the three needs to be multiplied by itself 7 times, giving us an answer of 2187.

Product of Powers Rule Rule: x a · x b = x a+b Example: 4 3 ·4 7 = 4 10

Power to a Power Rule Rule: (x a ) b = x a·b Example: (7 6 ) 2 = 7 12

Product of a Power Rule Rule: (x · y) a = x a · y a Example: (4 · 3) 7 = 4 7 · 3 7

Powers of a Fraction Rule Rule: Example:

Quotients of Powers Rule Rule: Example:

Zero Exponent Rule Rule: Example: 3 0 = 1

Negative Exponent Rule Rule: Example:

Rational Exponents Rule Rule: Example:

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