Radicals and Rational Exponents Review

Quick refresher into our exponent laws (index laws).

Index Law 1
Product Rule (Multiplication)

Multiple Choice

$$6^7\ \times6^2$$

• 6⁸

• 6¹⁴

• 6⁹

Multiple Choice

$$b^3\cdot b^4\cdot y^7\cdot b$$  

• $$b^3\cdot b^4\cdot y^7\cdot b$$  

• $$b^{14}$$  

• $$b^{84}$$  

• $$b^{49}$$  

Index Law
Quotient Rule (Division)

Multiple Choice

4⁷/4²

• 1

• 4⁹

• 4⁵

• 1⁹

Multiple Choice

Simplify.   $$\frac{x^{-4}}{x^3}$$  

• $$\frac{1}{x^7}$$  

• $$x^7$$  

• $$\frac{x^3}{x^4}$$  

Index Law
Power of a; power, product and quotient (Bracket)

Multiple Choice

(4²)³

• 16³

• 4⁵

• 4⁶

• 4¹

Multiple Choice

(4/2)³

• 4^3/2^3

• 4/8

• 4^3/2

• 4/2^3

Multiple Choice

(xd²)³

• x³d³

• x⁶d⁶

• x³d⁶

• x

Index Law
Zero, negative and fractional (Remaining laws)

Multiple Choice

Simplify

• $$\frac{1}{8}$$  

• -16

• $$\frac{1}{16}$$  

• 16

Multiple Choice

Simplify.

• y¹⁵
• y⁵
• y²
• 2y⁵

Multiple Choice

Write in index form
√x⁵

• X¹∕ ⁵

• X ²⁄⁵

• X⁵⁄ ²

• X⁵

Multiple Choice

Write the expression in root (radical) form.

x^3/4

• ∜x³

• ∛x⁴

• x^.75

• √x²

Multiple Choice

Write with a rational exponent.

• 7³

• 7

• 7^3/4

• 7^4/3

Multiple Choice

Write with a rational exponent.

HINT: what exponent is at the 2? It is "invisible"

• 2^1/6

• 64

• 6^1/2

• 2⁶

Multiple Choice

Write with a rational exponent.

HINT: what root is it? It is "invisible"

• 216

• 6^1/2

• 6²

• 6^3/2

Multiple Choice

∜m³ is the same as which answer?

• m^3/4

• m¹²

• m^4/3

• m⁷