Unit 6: Exponents Review

Exponent Rules

100

(8a^-2b⁵)⁰

1

200

x²x^-5/x³

1/x⁶

300

(5x²)^-3

1/125x⁶

400

(36x⁷y^-4)/(24x^-5y²)

3x¹²/2y⁶

500

(2x³)^-3(4x⁵y²)³

8x⁶y⁶

Solving Equations and Radical Form

100

Write in radical form.

x^3/5

5 root x³

200

Write in radical form, then simplify.

8^2/3

4

300

Write in radical form.

16^-3/4

1/

4 root 16³

400

Write in radical form and simplify.

(36x⁴)^3/2

sqrt(36x⁴)³

216x⁶

500

Write in radical form and simplify.

(243x¹⁵)^-2/5

1/fifth root of (243x¹⁵)²

1/9x⁶

Scientific Notation

100

Write in scientific notation.

567000

5.67 x 10⁵

200

Write the original number. 

3.62 x 10^-4

0.000362

300

Multiply the following numbers in scientific notation.

(3.2x10⁴)(1.5x10^-2)

4.8x10²

400

The population of Kansas City is about  5.1×10^5. The land area is about 3.19×10² sq. miles.  Write a fraction to represent the number of people per square mile. Then, approximate the value. 

(5.1x10⁵)/(3.19x10²)

=1.599x10³

500

Dallas, Texas has a land area of 3.405 x 10² square miles. The population of Dallas is 1.303 x 10⁶. Write a fraction to represent the number of people per square mile and then approximate the value. 

(1.303 x 10⁶)/(3.405 x 10²)

=3.827 x 10³

Solving Equations

100

Solve for x

x^3/4=343

x=2401

200

Solve for p

(p-19)³=343

p=26

300

Solve for v

4(v-2)⁵=972

v=5

400

5=-4+(x-26)^1/2

^{Solve for x.}

x=107

500

Solve for x

-8-3(x-12)^1/3=4

x=-52

Compound Interest

100

Suppose you invest $3,500 in a savings account that earns 7% interest, compounded quarterly. How much money would you have after 6 years? Round your answer to the nearest penny (hundredth)

$5307.55

200

If you deposit $5000 into an account paying 8.25% annual interest compounded continuously, how much money will be in the account after 15 years? round your answer to the nearest penny/hundredth

$17234.92

300

What will your account balance be in 6 months with an initial investment of $2500 compounded quarterly at a rate of 5%  ? round your answer to the nearest penny/hundredth

$2562.89

400

How much interest will you have in 6 years if you invest $1,000 at 3% compounded monthly? round your answer to the nearest penny/hundredth

$196.95

500

How much money do you need to invest at 2.8% compounded daily in order to have $25,500 at the end of 8 years?

Round to the nearest penny/hundredth

$20382.71