Exponents, Exponential Equations, & Growth/Decay

Properties of Exponents

100

Simplify the Expression. Use only positive exponents. (y³)(y^-5)

1/(y²)

200

Simplify the Expression. Use only positive exponents. (x⁴)/(x⁷)

1/(x³)

300

Simplify the Expression. Use only positive exponents. (x⁰y²)³

y⁶

400

Simplify the Expression. Use only positive exponents. (2x²/5y⁴)⁰

1

500

Simplify the Expression. Use only positive exponents. (2x²/5y⁴)^-2

25y⁸/4x⁴

Radicals and Rational Exponents

100

Evaluate the expression. √(25)

5

200

(8)^1/3

2

300

(-243)^1/5

-3

400

Evaluate the expression. 625^3/4

125

500

Evaluate the expression. √(-25)

No Solution

Growth & Decay

100

Does the function represent exponential growth or decay? Identify the percent change. f(t)=4(1.25)^t

growth, 25%

200

Does the function represent exponential growth or decay? Identify the percent change. f(t)=32(1.8)^t

Growth, 80 %

300

 Does the function represent exponential growth or decay? Identify the percent change. f(t)=2(0.25)^t

decay, 75%

400

A savings account balance is compounded

annually.  If the interest rate is 4% per

year and the current balance is $1,689.00,

what will the balance be 8 years from

now?

1689 (1.04 ^ 8) ≈ $2,311.51

500

An employee receives a 3% raise once per

year.  If the employee's initial salary is

$716,000, what will the employee's

salary be after 10 years?

A = 716000(1+.03)^10

$962,244.13

Solving Exponential Equations

100

Solve the equation. 5^x=5^3x-2

x=1

200

Solve the equation 3^x-2=1

x=2

300

(1/3)^(2x+3)=3

x=-2

400

27^2x+2=81^x+4

x=5

500

(1/16)^3x=64^2(x+8)

x=-4

Simplify Radicals

100

sqrt125

5sqrt5

200

(root(4)(3))^12

3^3 or 27

300

sqrt(36w^4)

6w^2

400

root(4)(81x^6y^3)

3xroot(4)(x^2y^3)

500

root(3)(4x^7y^2)

x^2root(3)(4xy^2)