Simplifying Exponents and Radicals

Simplify

 $\frac{\left(2xy^{-3}\right)^4}{\left(8x^{-6}y^3\right)^{\frac{2}{3}}}$  

•  $\frac{2x^4}{y^{10}}$  

•  $\frac{4x^8}{y^{14}}$  

•  $\frac{2}{y^{14}}$  

•  $\frac{4x^8}{y^9}$  

Tags

CCSS.HSN.RN.A.2

Simplify

 $^4\sqrt{81x^8y^7z^{10}}$  

•  $3x^2yz^2\ \ ^4\sqrt{y^3z^2}$  

•  $3x^4yz^4\ ^4\sqrt{y^3z}$  

•  $9x^2yz^4\ \ ^4\sqrt{y^3z^2}$  

•  $9x^4yz^2\ ^4\sqrt{y^3z^2}$  

Let a, b, and c be real numbers with a< 0, b<0 and c>0. Determine the sign of

 $ab^2c^3$  

• Positive 

• Negative

• Not enough information to be determined

Tags

CCSS.7.EE.B.3

Let a, b, and c be real numbers with a<0, b<0 and c>0. Determine the sign of

 $\left(c-b\right)^5$  

• Positive

• Negative 

• Not enough information to be determined

Simplify

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

•  $4x^5y^{12}$  

•  $4x^5y^7$  

•  $12xy^{12}$  

•  $12xy^8$  

Tags

CCSS.HSA.APR.A.1

Simplify  $\left(\frac{xy^{-2}z^{-3}}{x^2y^3z^{-4}}\right)^{-3}$  

•  $\frac{y^{15}}{x^3z^3}$  

•  $\frac{x^3y^{15}}{z^3}$  

•  $\frac{y^3}{z^3}$  

•  $\frac{x^{12}y^{15}}{z^3}$  

Tags

CCSS.8.EE.A.1

 $^3\sqrt{\left(x^3y\right)^2y^8}$  

Simplify

•  $x^2y^2\ \ \ ^3\sqrt{y}$  

•  $x^2y^2\ \ ^3\sqrt{y^2}$  

•  $x^3y^3\ \ ^3\sqrt{y}$  

•  $x^2y^3\ \ ^3\sqrt{y}$  

 $\frac{\left(32x^5y^{-\frac{3}{2}}\right)^{\frac{2}{5}}}{\left(x^{\frac{5}{3}}y^{\frac{2}{3}}\right)^{\frac{3}{5}}}$  

Simplify

•  $\frac{4x}{y}$  

•  $\frac{4x^4}{y^{\frac{1}{5}}}$  

•  $\frac{2x}{y^{\frac{1}{5}}}$  

•  $\frac{2x^4}{y}$  

Tags

CCSS.HSA.APR.A.1