Exponentiation, nth root and rationalization

Solve using exponentiation properties:

 $\left(-\frac{2}{3}\right)^4$  

• 16/81

• 56

• 81/16

• 3

Tags

CCSS.8.EE.A.1

Solve using exponentiation properties:

 $\left(27x^6\right)^{-3}$  

•  $27^3x^{18}$  

•  $27^{-3}x^{-3}$  

•  $\frac{1}{27^3x^{18}}$  

•  $27x^{-9}$  

Tags

CCSS.8.EE.A.1

Solve using nth root properties:

 $\sqrt{16a^8b^{-2}}$  

•   $\frac{4a^4}{b}$  

•  $\frac{4a^4}{b^{-2}}$  
  

•  $\sqrt{4a^8b^{-1}}$  
  

•  $\sqrt{\frac{16a^2}{b^2}}$  
  

Tags

CCSS.8.EE.A.2

Solve using nth root properties:

 $\sqrt{\sqrt{625x^8y^{16}}}$  

•   $5x^2y^4$  

•  $\sqrt{625x^8y^4}$  
  

•  $\sqrt{5x^2y^4}$  
  

•  $5\sqrt{x^8y^{16}}$  
  

Rationalize the denominator $\frac{\left(12\right)}{y-\sqrt{x}}$  

•   $\frac{12\left(y+\sqrt{x}\right)}{y^2-x}$  

•  $12\frac{\left(\sqrt{x}+\sqrt{xy}\right)}{x}$  
  

•  $\frac{12\left(x+y\right)}{x-y}$  
  

•  $\frac{\left(\sqrt{x}+\sqrt{y}\right)}{x}$  
  

Rationalize the denominator $\frac{6}{3+\sqrt{7}}$  

•   $9+3\sqrt{7}$  

•  $\frac{6\left(3+\sqrt{7}\right)}{9}$  
  

•  $3\left(\sqrt{7}+2\right)$  
  

•  $\frac{\left(\sqrt{3}+\sqrt{7}\right)}{2}$  
  

Tags

CCSS.HSN.RN.A.2

Rationalize the denominator $\frac{3}{\sqrt{5}}$  

•   $\frac{3\sqrt{5}}{5}$  

•  $\frac{\left(3+\sqrt{7}\right)}{5}$  
  

•  $3\sqrt{5}$  
  

•  $\frac{\left(\sqrt{5}+3\right)}{5}$  
  

Tags

CCSS.HSN.RN.A.2

Write in lowest terms $\sqrt{\left(\frac{2}{3}\right)^3}$  . Tip: Don't write the root as an exponent.

•   $\frac{2}{3\ }•\sqrt{\frac{2}{3}}$  

•  $\frac{2}{9\ }•\sqrt{\frac{2}{3}}$  
  

•  $\frac{4}{9\ }•\sqrt{\frac{4}{3}}$  
  

•  $\frac{\left(\sqrt{4}+3\right)}{3}$  
  

Tags

CCSS.HSN.RN.A.2

Using exponents properties, write in lowest terms

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

•  $\frac{xy}{z^2}$  

•  $\frac{x^2y}{z^2}$  

•  $\frac{x}{y^2z^2}$  

•  $\frac{x}{y^4z^2}$  

Tags

CCSS.8.EE.A.1

Using exponent's properties, write in lowest terms.

 $\left(3x^{3\ }y^{-6}\right)^2$  

•  $\frac{3x^6}{y^6}$  

•  $\frac{9x^6}{y^6}$  

•  $\frac{9x^6}{y^{12}}$  

•  $3x^{6\ }y^{12}$  

Tags

CCSS.8.EE.A.1