Rationals and Radicals

Which of the following is equivalent to 

 $\frac{1}{a^n}$  ?

•  $a^{-n}$  

•  $\sqrt{a}$  

•  $a^{\frac{1}{n}}$  

•  $-a^n$  

Which of the following is equivalent to

 $\frac{a^m}{a^n}$  ?

•  $a^{m-n}$  

•  $\sqrt{a^m}$  

•  $a^{\frac{m}{n}}$  

•  $man$  

Which is equivalent to the following... ?

• $x^{\frac{3}{5}}$

• $x^{\frac{5}{3}}$

• $\frac{3}{x^5}$

• $3x^5$

Which is equivalent to the following... ?

• $3\left(x^{\frac{5}{4}}\right)$

• $3\left(x^{\frac{4}{5}}\right)$

• $\frac{3}{x^5}$

• $3x^5$

Which is equivalent to the following...  $8^{\frac{4}{3}}$  ?

• 16

• 64

• 1/16

• 4

Which is equivalent to the following...  $\left(5^3\right)^2$  ?

•  $5^6$  
  

•  $5^5$  
  

•  $5^{\frac{3}{2}}$  
  

•  $5^{32}$  
  

Which is equivalent to the following...  $\left(4^{-1}\right)^2$  ?

• 1/16

• -16

• 1/8

• -1/16

Which of the following is not equivalent to each other?  (Which one is not like the others?)

•  $x^{\frac{10}{4}}$  
  

•  $x^{\frac{5}{2}}$  
  

•  $x^2\sqrt{x}$  

•  $x\sqrt{x}$  
  

Solve for x. $3x^3=375$  

• x = 5

• x = 3

• x = -5

• x = 25

Solve for x. $\left(x-4\right)^4=256$  

• x = 8 and x = 0

• x = 8

• x = 8 and x = -8

• x = 0 and x = 4