Exponents including Power to a Power

SImplify the following:  $\left(5^4\right)^3$  

•  $5^7$  

•  $5^{12}$  

•  $125^7$  

•  $125^{12}$  

Simplify the following:  $\left(2x\right)\left(x^4\right)$  

•  $2x^4$  

•  $3x^4$  

•  $2x^5$  

•  $3x^5$  

Simplify the following:  $\left(3x^2\right)^2$  

•  $3x^4$  

•  $6x^4$  

•  $9x^4$  

•  $81x^4$  

Which of the following statements correctly simplifies the two expressions:  $\left(2^2\right)\left(2^3\right)$   and  $\left(2^2\right)^3$  ?

• the first expression simplifies to  $2^5$  , while the second expression simplifies to  $2^6$  .

• the first expression simplifies to  $2^6$  , while the second expression simplifies to  $2^5$  .

• both expressions simplify to  $2^5$  .

• both expressions simplify to  $2^6$  .

 Which of the following statements correctly simplifies the two expressions:  $\left(5x^2\right)\left(5x^2\right)$  and  $\left(5x^2\right)^2$  ?

• the first expression simplifies to  $10x^4$ , while the second expression simplifies to  $25x^4$  .

• the first expression simplifies to  $25x^4$  , while the second expression simplifies to  $10x^4$  .

• both expressions simplify to  $10x^4$  .

• both expressions simplify to  $25x^4$  .

Simplify the following variable expression: $\frac{\left(3x\right)^3}{3x^3}$  (assuming  $x\ \ne\ 0$  )

• 0

• 1

• 3

• 9

 $\left(x^5\right)\left(x^2\right)^3$  Simplify the following expression:

•  $x^{10}$  

•  $x^{11}$  

•  $x^{17}$  

•  $x^{30}$  

Simplify the following expression:  $\left(-2x^3\right)^3$  

•  $-6x^6$  

•  $-8x^6$  

•  $-6x^9$  

•  $-8x^9$  

Simplify the following expression:  $\left(4x^2\right)\left(3x^3\right)^2$  

•  $12x^7$  

•  $12x^8$  

•  $36x^8$  

•  $144x^{10}$  

Which of the following expressions will always equal ONE? (assuming  $x\ \ne\ 0$  )

•  $\frac{16x^2}{\left(4x\right)^2}$  

•  $\frac{\left(3x^3\right)^2}{9x^5}$  

•  $\frac{\left(2x\right)\left(4x\right)}{6x}$  

•  $\frac{\left(x^3\right)^3}{\left(x^4\right)^2}$