Rational Exponents

Simplify . Your answer should contain only positive exponents.  $4v^{\frac{2}{3}}\cdot v^{-1}$  
  

•  $4v^{\frac{1}{3}}$  

•  $\frac{4}{v^{\frac{1}{3}}}$  

•  $\frac{v^{\frac{1}{3}}}{4}$  

•  $\frac{1}{4v^{\frac{1}{3}}}$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify . Your answer should contain only positive exponents.  $\frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{2x^{\frac{4}{3}}y^{-\frac{7}{4}}}$  

•  $\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$  

•  $\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$  

•  $\frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$  

•  $\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$  

Tags

CCSS.HSA.APR.A.1

Evaluate the expression WITHOUT using a calculator:  $64^{-\frac{2}{3}}$  

•  $\frac{1}{16}$  

•  $\frac{1}{512}$  

• -16

• -512

Evaluate the expression WITHOUT a calculator:  $36^{\frac{3}{2}}$  

• 144

• -144

• 216

• -216

Evaluate the expression WITHOUT using a calculator: $\left(-32\right)^{\frac{2}{5}}$  

•  $-\frac{1}{4}$  

•  $\frac{1}{4}$  

• -4

• 4

Rewrite with a radical

 $x^{\frac{5}{4}}$  

•  $\sqrt[4]{x^5}$  

•  $\sqrt[5]{x^4}$  

•  $\sqrt[4]{x}$  

• None are correct

 $\sqrt{\sqrt[3]{x}}$  

•  $x^{\frac{1}{6}}$  

•  $x^{\frac{2}{3}}$  

•  $x^{\frac{1}{5}}$  

•  $x^{\frac{3}{2}}$  

 $\left(\frac{m^8}{n^{12}}\right)^{-\frac{1}{4}}$  

•  $\frac{n^3}{m^2}$  

•  $\frac{m^4}{n^8}$  

•  $\frac{n^8}{m^4}$  

• Not here

 $\left(\sqrt[5]{-32}\sqrt[3]{x^9}\right)^4$  

•  $-2x^{12}$  

•  $16x^{12}$  

•  $16x^7$  

•  $-2x^{\frac{3}{4}}$  

 $\sqrt{48^3x^6y^2}$  

Rewrite

•  $48^{\frac{2}{3}}x^4y$  

•  $48^{\frac{3}{2}}x^3y$  

•  $48^{\frac{3}{2}}x^4y^0$  

• None are correctly rewritten