Ch 6 Rational Exponents Exam

Simplify; use absolute value where needed.

 $\sqrt{24x^6y^{20}}$  

•  $4x^3y^{10}\sqrt{6}$  

•  $2\left|x^3\right|y^{10}\sqrt{6}$  

•  $2\left|x^3y^6\right|\sqrt{6}$  

•  $2x^3\left|y^6\right|\sqrt{6}$  

Simplify. Rationalize all denominators. Assume all variables are positive.

 $\frac{4-\sqrt{7x}}{\sqrt{18x}}$  

•  $\frac{4\sqrt{2x}-x\sqrt{14}}{6x}$  

•  $\frac{4\sqrt{2x}-\sqrt{14x}}{6x}$  

•  $\frac{2\sqrt{2x}-x\sqrt{14}}{3x}$  

•  $\frac{4\sqrt{x}-x\sqrt{14x}}{18x}$  

Given than x > 1 and y > 1, which of the following is equivalent to

 $\frac{x^{-2}y^{\frac{1}{2}}}{x^{\frac{1}{3}}y^{-1}}$  

• 
• 
• 
• 

 $If\ x^{-\frac{1}{2}}=\frac{1}{8},\ what\ is\ the\ value\ of\ x^{\frac{2}{3}}?$  

•  $\frac{1}{2}$  

•  $\frac{1}{4}$  

• 4

• 16

 $If\ k,\ n,\ x,\ and\ y\ are\ positive\ numbers\ such\$ 
 $that\ x^{-\frac{4}{3}}=k^{-2}\ and\ y^{\frac{4}{3}}=n^2,\$  

 $what\ is\ \left(xy\right)^{-\frac{2}{3}}in\ terms\ of\ n\ and\ k?$  

•  $\frac{1}{nk}$  

•  $\frac{n}{k}$  

•  $\frac{k}{n}$  

•  $nk$  

Which of the following is equivalent to


 $\frac{\left(x^2y\right)^3}{x^7y^2}\sqrt{xy}$  ?

•  $\frac{y^{\frac{3}{2}}}{x^{\frac{1}{2}}}$  

•  $x^{\frac{3}{2}}y^{\frac{1}{2}}$  

•  $x^{-\frac{3}{2}}y^{\frac{3}{2}}$  

• None of these

 $If\ 2^{\left(x+3\right)}-2^x=k\left(2\right)^x,\ what\ is\ the\ value\ of\ k?$  

• 3

• 5

• 7

• 8

Simplify within the real number system. 

 $\left(\frac{27e^3i^{-8}}{81e^{-6}i^{-4}}\right)^{-\frac{2}{3}}$  

•  $\frac{3i^{\frac{8}{3}}}{9e^6}$  

•  $\frac{i^{\frac{8}{3}}}{3e^6}$  

•  $\frac{i^6}{3e^6}$  

•  $\frac{-3i^6}{e^{\frac{8}{3}}}$  

Solve for x:  

 $4\left(3x-3\right)^{\frac{2}{3}}=36$  

• 10

• -8, 10

• 0, 10

• -8

Given the functions below, find 

 $-2f\left(x\right)-3g\left(x\right):\$  

 $f\left(x\right)=2x-3\ \ \ and\ \ \ \ g\left(x\right)=x^2-5x+1$  

•  $-3x^2+11x+3$  

•  $-3x^2-19x+9$  

•  $3x^2+11x+9$  

• None of these