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 × ... × A Examples 31 = 3 32 = 3 × 3 = 9 33 = 3 × 3 × 3 = 27 34 = 3 × 3 × 3 × 3 = 81

Bellwork Grab a new bellwork sheet Simplify the following into exponential notation: 28 x 28 52 x 527 3x…x3= 12 times

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

Whole number exponential notation Write the following in exponential notation with a base number of 2: 8 16 128 256

Bellwork The area of Mrs. Stoecker’s garden is 146 ft squared. How long is one side of her garden? Is it a perfect square? Simplify if possible: X2y5(y3)(X3y) 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 (x2)4  = (x2)(x2)(x2)(x2) or (xx)(xx)(xx)(xx)  = x8

continued

Bellwork (-6) x … x (-6) = −6 4 Is this in correct notation? Why or why not 75 × 7x = 713 What is x? Simplify if possible, if cant tell why: 𝑎 10 𝑏 10 𝑥 7 5

What if the problem were upside down? 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.

Continued 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. Ex: 4-2 = 𝟏 42 or 𝟏 𝟏𝟔

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

Zero Exponent A Zero exponent is investigated in much the same way.   ,   as lo 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: