 # Laws of Exponents. 5 2 = 5 x 5 =25 3 4 =3 x 3 x 3 x 3 = 81 7 3 = 7 x 7 x 7 = 343.

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Laws of Exponents

5 2 = 5 x 5 =25 3 4 =3 x 3 x 3 x 3 = 81 7 3 = 7 x 7 x 7 = 343

5 2 x 5 4 (5 x 5)(5 x 5 x 5 x 5) = 5 6 Do you see a pattern or shortcut?

3 3 x 3 5 (3x3x3)(3x3x3x3x3) = 3 8 Do you see a pattern or shortcut?

a 3 x a 5 (a x a x a)(a x a x a x a x a) = a 8 Do you see a pattern or shortcut?

Product of Powers Property To multiply powers (exponents) with the same base, add their exponents. a³ x a²= a 3 + 2 = a 5

2525 2323 = 2 x 2 x 2 x 2 x 2 2 x 2 x 2 = 2 1 4545 4242 = 4 x 4 x 4 x 4 x 4 4 x 4 = 4343 1 Do you see a pattern or shortcut?

Quotient of Powers Property To divide powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. 6 8 = 6 8-5 =6 3 6 5

REVIEW When multiplying- add the exponents When dividing- subtract the exponents.

EXAMPLES 2 3 2 2 = 69=69= 6464 z5z5 b 10 2525 6565 b 7 b 3 = Z 8 = z 3

Zero Exponents For any nonzero number a, a 0 = 1 Anything to the zero power equals 1 (except zero) 4 0 = 100 0 = 1 1

Negative Exponents For any nonzero number a and any integer n, a -n = 1/a n 5 -2 = 1 5252

3 -5 = 1 3535 5 -2 = 1 5252 3y -2 =3 y2y2 a -7 b 3 =b3b3 a7a7

5 -8 x 5 -3 = 5 -8 + -3 =5 -11 5 11 1 or a -2 x a 10 = a -2 + 10 =a8a8

b -8 x b 5 = b -8 + 5 =b -3 b3b3 1 or 3 -4 x 3 11 = 3 -4 + 11 =3737

3535 3838 = 3 5 - 8 = 3 -3 or 1 3 a6a6 a -2 = a 6 – (-2) = a8a8 m2m2 m -4 = m 2 – (-4) = m6m6

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