Exponent Rules

Product Property of Exponents

100

Write the expression as a single exponent expression.

(4⁶)(4⁸)

4¹⁴

200

Write the expression as a single exponent expression.

(x^5*y^7)/(x^3*y^2)

x²y⁵

300

Write the expression as a single exponent expression.

(336²)(336²⁸)

336³⁰

400

Write the expression as a single exponent expression.

25^17 * 25^36

25⁵³

500

Write the expression as a single exponent expression.

(9^-4)(9¹⁶)

9¹²

Power of a Power Property of Exponents

100

Write the expression as a single exponent expression.

(2⁴)³

2¹²

200

Write the expression as a single exponent expression.

(6⁵)⁴

6²⁰

300

Write the expression as a single exponent expression.

(18⁶)⁷

18⁴²

400

Write the expression as a single exponent expression.

(270³)¹²

270³⁶

500

Write the expression as a single exponent expression.

(49²⁷)²

49⁵⁴

Quotient Property of Exponents

100

Write the expression as a single exponent expression.

4^6/4^5

4¹ or 4

200

Write the expression as a single exponent expression.

56^4/56^4

56⁰ or 1

300

Write the expression as a single exponent expression.

16^18/16^5

16¹³

400

Write the expression as a single exponent expression.

12^3/12^5

12^-2 or 1/12^2

500

Simplify

(54x^8z^6)/(6x^2z^3)

9x^6z^3

Power of a Product Property of Exponents

100

Simplify

(4x)⁴

4⁴x⁴

200

Simplify

(5x²)⁴

5⁴x⁸

300

Simplify

(3x²y³)⁰

1

400

Simplify

(3xy²)³

3³x³y⁶

500

Simplify

(5x²yz³)⁴

5⁴x⁸y⁴z¹²

Power of a Quotient Property of Exponents

100

Simplify 

(x/y)^2

x^2/y^2

200

Simplify 

(3/4)^2

 3^2/4^2 or 9/16

300

Simplify

(w/p)^2

w^2/p^2

400

Simplify

((3x)/y)^2

(3^2x^2)/y^2

500

Simplify

(1/4)^2

1^2/4^2 or 1/16

Random

100

Simplify

364,805⁰

1

200

Rewrite with only positive exponents

15^-3

1/15³

300

There are about 10¹¹ stars in the Milky Way Galaxy. There are about 10¹² galaxies in the universe. Assuming the Milky Way Galaxy is about average for the number of stars it contains, how many stars are there in the universe? 

10²³ or 100 billion trillion, or 100 sextillion.

400

In 2021 about 4²¹ kilowatthours of electricity were generated in the United States. In 2021 there were about 4¹⁴ people in the United States. How many kilowatthours of energy did each person use?

4⁷ or 16384 kilowatt hours per person

500

In 2021 Spotify had about 5¹² premium subscribers. The annual cost for a premium subscription is about $5³. How much money did Spotify make from premium subscriptions in 2021?

$5¹⁵