Exponents - Unit 5

Exponent Laws

100

x² • x⁴

x⁶

200

5² • 5 • 5²

5⁵ or 3125

300

[(-2)³]⁴

(-2)¹²  or 4096

400

-8a⁵ • (2a³)²

-32a¹¹

500

(3/4)³ • (3/4)²  /  (3/4)⁵

(3/4)⁰  or 1

Rational Exponents

100

Rewrite: x^1/2

√x

200

Rewrite: x^4/9

⁹√x⁴

300

Solve: ⁵√-32

-2

400

Solve: (-27)^-1/3

-1/3

500

(y^1/4)²  • (y^-1/3)²

1/y^1/6

Equivalent Expressions

100

Solve into positive exponents: 1/x^-4

x⁴

200

True or False: g(x)=16^3x  equals  f(x)= 4^6x

TRUE

300

T or F: g(x)=16^3x  equals  h(x)=62^2x

FALSE: 64^2x

400

Solve an equivalent expression: 1/4^-3/2

8

500

Is f(x)= (8x)^3/2(x^5/2) equivalent to g(x)= (√8)³x⁴

Yes: f(x)=g(x)

Solving Exponential Equations

100

5x = x + 12

4x = 12 or x = 3

200

2^x = 2⁵

x = 5

300

5^x = 1/25

x = -2

400

5^8x+1 = 5^-2x+21

x = 2

500

5^3x-1 = 125^-2x

x = 1/a

Mixed Exponents

100

True or False: x²  • x³ = x⁶

FALSE: x⁵

200

Simplify: (y³)²

y⁶

300

Evaluate: 10³

1000

400

Evaluate: 16^1/2

4

500

(x⁴)³ / x³

x⁹