Rational Exponents

Unit 6-Radical Functions

Rational Exponents

Multiple Choice

Write the expression in radical form:
 $3^{\frac{5}{4}}$  

•  $^5\sqrt{3^4}$  

•  $^4\sqrt{3^5}$  

•  $\sqrt{3^4}$  

•  $\sqrt{3^{\frac{5}{4}}}$  

Multiple Choice

Write the expression in radical form:
 $\left(ab\right)^{\frac{3}{4}}$  

•  $^4\sqrt{\left(ab\right)^3}$  

•  $^4\sqrt{\left(ab^3\right)}$  

•  $^3\sqrt{\left(ab\right)^4}$  

Multiple Choice

Write the expression in radical form:
 $\left(-6x\right)^{\frac{2}{3}}$  

•  $^3\sqrt{\left(-6x\right)^2}$  

•  $^3\sqrt{36x^2}$  

•  $^3\sqrt{-6^2x^2}$  

Multiple Choice

Write the expression in radical form:
 $7\left(12w\right)^{\frac{1}{2}}$  

•  $7\sqrt{12w}$  

•  $\sqrt{84w}$    

•  $14\sqrt{3w}$  
  

Multiple Choice

Write the expression in exponential form:

 $^4\sqrt{k^5}$  

•  $k^{\frac{5}{4}}$  

•  $k^{\frac{4}{5}}$  

•  $\frac{k^4}{5}$  

Multiple Choice

Write the expression in exponential form:
 $\left(\sqrt{3m}\right)^7$  

•  $\left(\sqrt{3m}\right)^{\frac{1}{2}}$  

•  $\left(\left(3m\right)^{\frac{1}{2}}\right)^7$  

•  $\left(3m\right)^{\frac{7}{2}}$  

•  $3m^{\frac{7}{2}}$  

Multiple Choice

 $\left(^4\sqrt{-2a}\right)^5$  

Select the process and answer that best simplifies this expression:

•  $\left(\left(\sqrt{-2a}^{\frac{1}{4}}\right)^5\right)=\left(\sqrt{-2a}\right)^{\frac{5}{4}}$  

•  $\left(\left(\sqrt{-2a}\right)^{\frac{1}{4}}\right)^5=\left(\sqrt{-2a}\right)^{\frac{5}{4}}$  

•  $\left(^4\sqrt{-2a}\right)^5=\left(\sqrt{-2a}^{\frac{1}{4}}\right)$  

Multiple Choice

Write in exponential form:
 $^3\sqrt{9x^7y^4}$  

•  $9^{\frac{1}{3}}x^{\frac{7}{3}}y^{\frac{4}{3}}$  

•  $x^2y\left(9xy\right)^{\frac{1}{3}}$  

•  $\left(9x^7y^4\right)^{\frac{1}{3}}$  

Multiple Choice

Simplify the expression:
 $\left(-216\right)^{-\frac{1}{3}}$  

•  $-\frac{1}{6}$  

•  $^3\sqrt{216}$  

•  $-^3\sqrt{-216}$  

•  $\frac{1}{^3\sqrt{-216}}$  

Multiple Choice

Simplify the expression:
 $^3\sqrt{v}\times\sqrt{v}$  

•  $v^{\frac{5}{6}}$  

•  $^5\sqrt{v^6}$  

•  $^6\sqrt{v^5}$  

•  $v^{\frac{1}{3}+\frac{1}{2}}$  

Multiple Choice

Select the next best step for this expression:

 $\frac{4}{^3\sqrt{4}}$  

• 1

•  $\frac{4}{4^{\frac{1}{3}}}$  

• Cannot do this operation

Multiple Choice

Select the next best step for this expression:

 $\frac{4}{^3\sqrt{4}}=\frac{4}{4^{\frac{1}{3}}}$  

•  $4^1\div4^{\frac{1}{3}}=4^{1-\frac{1}{3}}$ 

•  $4^1\div4^{\frac{1}{3}}=4^{1\div\frac{1}{3}}$  

• Cannot do this operation

Multiple Choice

Select the answer to this expression:

 $\frac{4}{^3\sqrt{4}}=\frac{4}{4^{\frac{1}{3}}}=4^1\div4^{\frac{1}{3}}=4^{1-\frac{1}{3}}$  

•  $4^0$ 

•  $4^{\frac{2}{3}}$  

•  $^3\sqrt{4^2}$  
  

• Cannot do this operation

Multiple Choice

Simplify the expression: $^4\sqrt{x^{10}}$  

•  $x^{\frac{5}{2}}$  

•  $\sqrt{x^5}$  

•  $x^2\sqrt{x}$  

•  $x^{2\ \ 4}\sqrt{x^2}$