Radical and Fractional exponents

Unit 3: Radicals

By Crissy Matlick

Match

Match the following exponent rules:

• Product Rule: $$x^a\cdot x^b=$$

• Power Rule:

  $$\left(x^a\right)^b=$$

• Quotient Rule:

  $$\frac{x^a}{x^b}=$$

• Negative exponent rule

  $$x^{-a}=$$

• Zero exponent rule:

  $$x^0=$$

• $$x^{\left(a+b\right)}$$

• $$x^{ab}$$

• $$x^{\left(a-b\right)}$$

• $$\frac{1}{a}$$

• $$1$$

Labeling

Label the image using the following words:

Drag labels to their correct position on the image

radical

radicand

index

exponent

n=2

expression

Match

Match the following radical forms with their corresponding rational exponent forms

• $$\sqrt[3]{x^4}$$

• $$\sqrt[4]{x^8}$$

• $$\left(\sqrt[8]{11w}\right)^6$$

• $$\frac{1}{\sqrt[]{w}}$$

• $$x^{\frac{4}{3}}$$

• $$x^2$$

• $$\left(11w\right)^{\frac{3}{4}}$$

• $$w^{-\frac{1}{2}}$$

Match

Match the following rational exponents with their simplified version using the laws of exponents

• $$x^{\frac{1}{5}}\cdot x^{\frac{3}{5}}$$

• $$\frac{x^{\frac{5}{3}}}{x^{\frac{1}{3}}}$$

• $$\frac{\left(x^{\frac{2}{3}}\cdot x^{-\frac{1}{2}}\right)}{x^{\frac{1}{6}}}$$

• $$\left(a^{\frac{1}{4}}\right)^4$$

• $$\left(x^{\frac{3}{4}}\right)^{\frac{2}{5}}$$

• $$x^{\frac{4}{5}}$$

• $$x^{\frac{4}{3}}$$

• $$x$$

• $$a$$

• $$x^{\frac{3}{10}}$$

Math Response

Simplify the following rational exponent:

$$\left(\frac{a^{\frac{1}{6}}}{a^{-\frac{2}{3}}}\right)^2$$

Type answer here

Correct Answer: a^{\frac{10}{12}}

Deg^°

Rad

Match

Rewrite the following using fractional exponents

• $$\sqrt[5]{\left(2x\right)^{10}}$$

• $$\sqrt[3]{27x^4y^6}$$

• $$\left(\sqrt[6]{w^2}\right)\left(\sqrt[3]{w}\right)$$

• $$\frac{\sqrt[3]{p^5}}{p\sqrt[3]{p}}$$

• $$4x^2$$

• $$3x^{\frac{4}{3}}y^2$$

• $$w^{\frac{2}{3}}$$

• $$p^{\frac{1}{3}}$$