Rational Exponents Review

On Desmos, graph to solve the following equation for x:

 $\sqrt{2x+5}=\left|x-2\right|+3$  

•  $x=4.828$  

•  $x=2$  

•  $x=3$  

•  $No\ Solution$  

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.D.11

 $\frac{2}{5}\sqrt{4x-5}=2$  

Solve for x.

•  $x=1.25$  

•  $x=3.75$  

•  $x=7.5$  

•  $x=2.5$  

Tags

CCSS.HSA.REI.A.2

Rewrite in radical form.

 $\left(n^2\right)^{\frac{2}{3}}$  

•  $\ ^4\sqrt{n^3}$  

•  $\ ^3\sqrt{n^4}$  

•  $\ ^3\sqrt{n}$  

•  $\sqrt{n^3}$  

Tags

CCSS.HSN.RN.A.2

Rewrite in radical form.

 $\frac{\left(2x\right)^{\frac{1}{3}}}{\left(3y\right)^{\frac{3}{4}}}$  

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

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

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

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

Tags

CCSS.HSN.RN.A.2

Rewrite in exponential form.

 $\ ^3\sqrt{6^4}$  

•  $6^{\frac{1}{12}}$  

•  $6^{\frac{1}{7}}$  

•  $6^{\frac{3}{4}}$  

•  $6^{\frac{4}{3}}$  

Tags

CCSS.HSN.RN.A.2

Rewrite in exponential form.

 $\ ^{6\sqrt{\left(7x\right)^5}}$  

•  $7x^{\frac{6}{5}}$  

•  $7x^{\frac{5}{6}}$  

•  $\left(7x\right)^{\frac{6}{5}}$  

•  $\left(7x\right)^{\frac{5}{6}}$  

Tags

CCSS.HSN.RN.A.2

Rewrite with no negative exponents in simplest radical form.

 $5y^{-3}$  

•  $\frac{5}{\ ^{3\sqrt{y}}}$  

•  $\frac{1}{^{\ 3}\sqrt{5y}}$  

•  $\frac{5}{y^3}$  

•  $\frac{1}{5y^3}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSN.RN.A.2

Rewrite with no negative exponents in simplest radical form.

 $\left(\frac{x^2}{x^5}\right)^{-\frac{1}{4}}$  

•  $\ ^4\sqrt{x^3}$  

•  $\ ^3\sqrt{x^4}$  

•  $\ ^4\sqrt{x^7}$  

•  $\ ^7\sqrt{x^4}$  

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Rewrite with no negative exponents in simplest radical form.

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

•  $\ ^5\sqrt{x^{12}}$  

•  $\ ^{12}\sqrt{x^5}$  

•  $\ ^6\sqrt{x^7}$  

•  $\ ^7\sqrt{x^6}$  

Tags

CCSS.HSN.RN.A.2

Rewrite with no negative exponents in simplest radical form.

 $\left(\frac{m^4}{m^{\frac{1}{2}}}\right)^{\frac{1}{4}}$  

•  $\ ^5\sqrt{m^6}$  

•  $\ ^6\sqrt{m^5}$  

•  $\ ^8\sqrt{m^7}$  

•  $\ ^7\sqrt{m^8}$  

Tags

CCSS.HSN.RN.A.2