Algebra 2 - 5.1 Roots, radicals, rational exponents

Simplify

 $^4\sqrt{\frac{625x^{11}}{16y^8}}$  

•  $\frac{156.26x^7}{4y^4}$  

•  $\frac{156.25\ x^2\ ^4\sqrt{x^3}}{4y^2}$  

•  $\frac{5\ x^2\ ^4\sqrt{x^3}}{2y^2}$  

•  $\frac{5\ x^7}{2y^4}$  

Three different expressions are simlified below. Only one of them is done correctly. Which option does NOT contain an error?

• $100^{-\frac{1}{2}}=\sqrt{-100}=\ \pm10i$

• $9^{-\frac{2}{3}}=9^{\frac{3}{2}}=\left(\sqrt{9}\right)^3=27$

• $25^{-\frac{3}{2}}=\left(\sqrt{\frac{1}{25}}\right)^3=\frac{1}{125}$

Simplify

 $2\sqrt{6}\left(3\sqrt{2}-\sqrt{10}\right)+4\sqrt{3}$  

•  $16\sqrt{3}-4\sqrt{15}$  

•  $8\sqrt{12}-5\sqrt{60}$  

•  $4\sqrt{48}$  

•  $10\sqrt{2}-8+4\sqrt{3}$  

Three different expressions are simplified below. Only one of the expressions is simplified correctly. Which expression does NOT contain an error?

• $\sqrt{4x^2+9}=\sqrt{4x^2}+\sqrt{9}=2x+3$

• $\sqrt{9x^2+12x+4}=\sqrt{\left(3x+2\right)^2}=3x+2$

• $\left(4x+10\right)^2=\left(4x\right)^2+10^2=16x^2+100$

Simplify by rationalizing the denominator:

 $\frac{3}{^3\sqrt{2y}}$  

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

•  $\frac{3^{\ \ \ \ 3}\sqrt{4y^2}}{2y}$  

•  $\frac{3\ \ \ ^3\sqrt{2y}}{8y^3}$  

•  $\frac{3\ \ ^3\sqrt{4y^2}}{8y^3}$  

Solve for x:

 $8^{-2x}=2^{x+3}$  

Write your fractional answer in the form top/bottom.

Solve for x:

 $4^{x+3}=\left(\frac{1}{2}\right)^{2-x}$