WB pg. 176

WB pg. 176

WB pg. 176 Write in exponential form

WB pg. 177

WB pg. 177

WB pg. 177 Evaluating expressions

WB pg. 178

WB pg. 178 Guided practice

WB pg. 178 Guided practice KEY

WB pg. 179 Independent practice

WB pg. 179 Independent practice KEY

WB pg. 179 Independent practice

WB pg. 179 Independent practice KEY

If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power. Exponent Base 7 2

The factors of a power, such as 74, can be grouped in different ways The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

Also know as the laws of exponents: Product rule (multiply monomials) Quotient rule (divide monomials) WB pgs. 183- 190

WB pg. 184

Product Rule: Same base, add exponents.

WB pg. 184

WB pg. 184

WB pg. 185

WB pg. 185

WB pg. 185 KEY

WB pg. 186

WB pg. 186

WB pg. 186 KEY

WB pg. 187 Independent practice

WB pg. 187 KEY

WB pg. 187

WB pg. 186 KEY

Ex’s : Multiplying Powers with the Same Base Multiply. Write the product as one power. 1. 66 • 63 6 6 + 3 Add exponents. 6 9 2. n5 • n7 n 5 + 7 Add exponents. n 12

Ex’s: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. 3. 25 • 2 2 5 + 1 Think: 2 = 2 1 2 6 Add exponents. 4. 244 • 244 24 4 + 4 Add exponents. 24 8

5. 42 • 44 4 Add exponents. 4 6. x2 • x3 x Add exponents. x You try!!! Multiply. Write the product as one power. 5. 42 • 44 4 2 + 4 Add exponents. 4 6 6. x2 • x3 x 2 + 3 Add exponents. x 5

Cannot combine; the bases are not the same. You try!!! Multiply. Write the product as one power. 7. x5 • y2 Cannot combine; the bases are not the same. x5 • y2 8. 412 • 417 41 2 + 7 Add exponents. 41 9

Same base, subtract exponents. Quotient Rule: Same base, subtract exponents. Notice what occurs when you divide powers with the same base. 5 53 = 5  5  5 5  5  5  5  5 = 5 • 5 = 52

Ex’s : Dividing Powers with the Same Base Divide. Write the quotient as one power. 7 5 3 1. 7 5 – 3 Subtract exponents. 7 2 x 10 9 2. x 10 – 9 Subtract exponents. x Think: x = x 1

3. 4. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e Ex’s Divide. Write the product as one power. 9 9 3. 9 2 9 9 – 2 Subtract exponents. 97 e 10 4. e 5 e 10 – 5 Subtract exponents. e 5

5. 4. 3 3 3 Subtract exponents. 32 x x x Subtract exponents. x You try: Divide. Write the product as one power. 3 8 5. 3 6 3 8 – 6 Subtract exponents. 32 x 15 4. x 3 x 15 – 3 Subtract exponents. x 12

= 1 Zero Exponent Rule Any Base Any base raised to the zero power (except 0) is ALWAYS equal to one. Any Base = 1

Any number divided by itself is always 1. Why? Following the Quotient Rule: Any number divided by itself is always 1.

As known as the “power to power rule” WB pgs. 191 - 198

WB pg. 192

WB pg. 192

WB pg. 192

WB pg. 193

WB pg. 195 Independent practice

WB pg. 195 Independent practice KEY

Power raised to a power, multiply exponents. Power to a power Rule : Power raised to a power, multiply exponents. Reading Math (9 ) is read as “nine to the fourth, to the fifth.” 5 4

Ex’s: Raising a Power to a Power Simplify. 1. (54)2 (54)2 = 54 • 2 Multiply exponents. = 58 2. (67)9 (67)9 = 67 • 9 Multiply exponents. = 663

Ex’s: Raising a power to power Simplify. 3. (33)4 (33)4 = 33 • 4 Multiply exponents. = 312 4. (48)2 (48)2 = 48 • 2 Multiply exponents. = 416

Ex’s: Raising a Power to a Power Simplify. 2 3 12 3 5. 6. (172) 20 (172) 20 Multiply exponents. Multiply exponents. 2 3 12 • 3 = = 172 • 20 2 3 36 = = 1740

= = 7. 8. (134) 10 Multiply exponents. Multiply exponents. YOU TRY!!! Simplify. 1 4 11 2 7. 8. (134) 10 (134) 10 Multiply exponents. Multiply exponents. 1 4 11• 2 = = 134 • 10 1 4 22 = = 1340

Power of Product Rule: Product raised to a power, distribute power to each base. Evaluate the number(s)/coefficients. Multiply the exponents. (2x2y5)3 = 23x2*3y5*3 8x6y15

Ex’s : Power to a power rule 16a6b8 1. (4a3b4)2 = 2. (9x5y4)3 = 729x15y12

Ex’s: RAISING A POWER TO A POWER 3. (5a5b10)3 = 125a15b30 4. (4x7y9)4 = 256x28y36

You TRY!!! 5. (2x4y5)3 = 8x12x15 6. (6a4b6)3 = 216a12b18