Quiz about Properties of Rational Exponents Review

Question 1

Select ALL the statements that are true.

Expressions are simplified when:

Accepted Answer

There are NO fractional exponents in the denominator

Accepted Answer

There are NO negative exponents

Accepted Answer

All fractions are reduced

Accepted Answer

Coefficients are simplified

Answer

There are No fractional Exponents in the numerator

Question 2

Simplify the expression: $$b^{\frac{3}{4}}\cdot b^{\frac{1}{6}}$$ .

Accepted Answer

$$b^{\frac{11}{12}}$$

Answer

$$b^{\frac{2}{5}}$$

Answer

$$b^{\frac{1}{8}}$$

Answer

$$b^{\frac{1}{4}}$$

Question 3

Simplify the expression: $$\left( x^2 \cdot y^3 \right)^{\frac{1}{2}}$$ .

Accepted Answer

$$xy^{\frac{3}{2}}$$

Answer

$$xy^3$$

Answer

$$x^{\frac{5}{2}}y^{\frac{7}{2}}$$

Answer

$$x^{\frac{1}{2}}y^{\frac{3}{2}}$$

Question 4

Simplify the expression: $$\left( w^{-\frac{3}{9}} \right)^{-\frac{4}{9}}$$ .

Accepted Answer

$$w^{\frac{4}{27}}$$

Answer

$$\frac{1}{w^{\frac{7}{9}}}$$

Answer

$$w^{\frac{4}{3}}$$

Answer

$$w^{\frac{7}{9}}$$

Question 5

Simplify the expression: $$\left( p^{\frac{6}{12}} \right)^{\frac{1}{3}}$$ .

Accepted Answer

$$p^{\frac{1}{6}}$$

Answer

$$p^{\frac{1}{5}}$$

Answer

$$p^{\frac{5}{6}}$$

Answer

$$p^{\frac{2}{3}}$$

Question 6

Simplify the expression: $$\frac{8m^{\frac{3}{4}}}{2m^{\frac{1}{2}}}$$ .

Accepted Answer

$$4m^{\frac{1}{4}}$$

Answer

$$4m^{\frac{1}{2}}$$

Answer

$$6m^{\frac{1}{4}}$$

Answer

$$4m^{\frac{1}{3}}$$

Question 7

Simplify the expression: $$\frac{x}{x^{\frac{1}{3}}}$$ .

Accepted Answer

$$x^{\frac{2}{3}}$$

Answer

$$x^{\frac{4}{3}}$$

Answer

$$\frac{x^{\frac{2}{3}}}{x}$$

Answer

$$x^{\frac{1}{3}}$$

Question 8

Simplify the expression: $$\frac{6x^{\frac{1}{2}}}{3x^{\frac{3}{2}} y}$$ .

Accepted Answer

$$\frac{2}{x y}$$

Answer

$$\frac{2}{x^{\frac{1}{2}} y}$$

Answer

$$\frac{2x}{y}$$

Answer

$$\frac{2}{y}$$

Question 9

Simplify the expression: $$\left( \frac{x^{\frac{1}{2}} y}{x^{\frac{1}{4}}} \right)^4$$ .

Accepted Answer

$$xy^4$$

Answer

$$x^{3/2}y^4$$

Answer

$$x^{1/2}y^4$$

Answer

$$x^2y^4$$

Question 10

Simplify the expression: $$\left( \frac{a^{\frac{2}{3}}}{a^{\frac{1}{6}}} \right)^3$$ .

Accepted Answer

$$a^{\frac{3}{2}}$$

Answer

$$a^{\frac{5}{2}}$$

Answer

$$a^{\frac{1}{2}}$$

Answer

$$a^{\frac{4}{3}}$$

Question 11

Simplify the expression: $$\frac{6}{4x^{\frac{7}{4}}}$$ .

Accepted Answer

$$\frac{3x^{\frac{1}{4}}}{2x^2}$$

Answer

$$\frac{6x^{\frac{4}{7}}}{4x}$$

Answer

$$\frac{3x^{\frac{1}{4}}}{2x}$$

Answer

$$\frac{6x^{\frac{1}{4}}}{4x^2}$$

Question 12

Simplify the expression: $$y^{-\frac{8}{5}}$$ .

Accepted Answer

$$\frac{y^{\frac{2}{5}}}{y}$$

Answer

$$\frac{y^{\frac{5}{8}}}{y}$$

Answer

$$y^{\frac{8}{5}}$$

Answer

$$\frac{1}{y^{\frac{8}{5}}}$$

Question 13

Simplify the expression: $$\left( 9^{\frac{1}{2}} \right)^4$$ .

Accepted Answer

81

Answer

27

Answer

9

Answer

36

Question 14

Simplify the expression: $$\sqrt[4]{512y^8z^{11}}$$ .

Accepted Answer

$$4y^2z^2\sqrt[4]{2z^3}$$

Answer

$$4y^2z^2\sqrt[4]{8z^3}$$

Answer

$$8y^2z^2\sqrt[4]{z^3}$$

Answer

$$8x^2z^3\sqrt[4]{2z}$$

Question 15

Simplify the expression: $$\sqrt[3]{36k^2p^{-6}} \cdot \sqrt[3]{6k^4p^{-3}}$$ .

Accepted Answer

$$\frac{6k^2}{p^3}$$

Answer

$$216k^8p^{18}$$

Answer

$$72k^2p^3$$

Answer

$$\frac{6k^6}{p^9}$$

Question 16

Simplify the expression: $$\sqrt[5]{x^{10}y^{15}}$$ .

Accepted Answer

$$x^{2}y^{3}$$

Answer

$$x^{\frac{2}{5}}y^{\frac{3}{5}}$$

Answer

$$x^{\frac{3}{5}}y^{\frac{2}{5}}$$

Answer

$$x^{\frac{1}{2}}y^{\frac{3}{2}}$$

Properties of Rational Exponents Review

17 questions

Select ALL the statements that are true.
Expressions are simplified when:

There is an order we should use to simplify rational exponents.
Order the statements below.

When multiplying with likes bases, add the exponents.

Recall: Power to a Power
Multiply the exponents!

Multiply Exponents! Remember to simplify

DIVIDE COEFFICIENTS
SUBTRACT EXPONENTS

Apply Exponent Properties First! When dividing, Subtract exponents.
Do not "rationalize" denominator as your first step.

Remember to apply Exponent Properties First. So subtract the exponents on x. Then. take care of the negative exponent.

Note: I simplified inside the parenthesis first, but you can also distribute the exponent of 4 to ALL of the exponents then simplify (subtract) the exponents on x.

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