Precalculus Summer Review: Exponent Rules & Rational Exponents

Know the Rules

100

Which property is illustrated by a^m⋅aⁿ=a^m+n?

What is the Product of Powers Property?

200

Which property is shown by (b^m)ⁿ=b^mn?

What is the Power of a Power Property?

300

Which property is used in c^m÷cⁿ=c^m−n ?

What is the Quotient of Powers Property?

400

Which property is shown by (xy)ⁿ=xⁿyⁿ ?

What is the Power of a Product Property?

500

Which property is illustrated by a⁰=1, a≠0?

What is the Zero Exponent Property?

Power Play

100

Simplify: x²(x³)

What is x⁵?

200

Simplify: (y³)²

What is y⁶?

300

Simplify: (2a²b)³

What is 8a⁶b³?

400

Simplify: (m⁴)(m⁻²)

What is m²?

500

Simplify: (3x²y)⁴

What is 81x⁸y⁴?

Splitting Powers, Turning the Tables

100

Simplify: x⁵÷x²

What is x³?

200

Simplify: a⁻¹

What is    1/a ?

300

Simplify  y^7 / y^4 

What is y³?

400

Simplify:  2^5 / 2^8 

What is  1/8 ?

500

Simplify:  (3x^-2) / (6x^4 

What is  1/(2x^6) ?

Fraction Take Action

100

Rewrite using radicals:  x^(1/2 

What is  sqrt(x) ?

200

Simplify: 27^(1/3 

What is 3?

300

Simplify:  16^(3/4 

What is 8?

400

Rewrite using a single radical:  a^(2/3 

What is  root3(x^2 ?

500

Simplify:  81^(-1/4 

What is  1/3 ?

So You Think You're Smart

100

Simplify: (x^2y^3)^0 

What is 1?

200

Simplify:  (4/9)^(3/2) 

What is  8/27? 

300

Simplify:  2^(x+2)/(2^x) 

What is 4?

400

Simplify:  ((a^3b^-2)/(c^-1))^-2 

What is  (c^2b^4)/a^6 ? 

500

Simplify:  (16x^8)^(1/4) 

What is  2x^2?