What is an exponent The base A is

What is an exponent? • The base A is raised to the power of (n) is equal to the multiplication of A, n times: • A n = A ×. . . × A • • • Examples 31 = 3 32 = 3 × 3 = 9 33 = 3 × 3 = 27 34 = 3 × 3 × 3 = 81

Bellwork • Grab a new bellwork sheet • Simplify the following into exponential notation: 1. 28 x 28 2. 52 x 527 3. 3 x…x 3= 12 times

Multiplication Rule Same Base a n · a m = a n+m Multiplication rule (product Rule) If bases are the same, keep the base and add the exponents together 23 · 24 = 23+4 = 128

Whole number exponential notation • Write the following in exponential notation with a base number of 2: 1. 8 2. 16 3. 128 4. 256

Bellwork 1. The area of Mrs. Stoecker’s garden is 146 ft squared. How long is one side of her garden? Is it a perfect square? 2. Simplify if possible: • X 2 y 5(y 3)(X 3 y) • 312 x 57 x 3 x 510

Division • to divide two exponents with the same base, you keep the base and subtract the powers. • • 67 / 63

Exponent raised to a power • When you have an exponent raised to a exponent, you keep the base then multiply the exponents (or powers). • ( xm ) n = x m n • (x 2)4 • = (x 2)(x 2) or (xx)(xx) • = x 8

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Bellwork •

Negative Exponent What if the problem were upside down? A negative exponent means the base is on the wrong side of the fraction line, so you need to flip the base to the other side.

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Negative Exponents a -n = ( 1 ______ n a ) A nonzero base raised to a negative exponent is the reciprocal of the base raised to the positive exponent.

Zero Exponent , as long as A Zero exponent is investigated in much the same way. If we subtract the exponents, we get: If we cancel, we get: