Refresher: Exponents and Radicals

Refresher: Exponents and Radicals

SIMPLIFY EXPONENTS

 $\left(2x^3y\right)\cdot\left(-4x^{-1}y^5\right)=-8x^2y^6$   $\left(\frac{-3a^3}{a^{-2}}\right)^2=\frac{9a^6}{a^{-4}}=9a^{10}$  

Multiple Choice

Simplify: $-4x^5\cdot6x^{10}$  

•  $-24x^{15}$  

•  $2x^{15}$  

•  $-24x^{50}$  

•  $\frac{x^{15}}{24}$  

Multiple Choice

Simplify:   $\left(-3t^4\right)^2$  

•  $-9t^8$  
  

•  $9t^6$  
  

•  $9t^8$  
  

•  $6t^8$  
  

Multiple Choice

Simplify the following expression:

xy^-7

• xy⁷

• $\frac{x}{y^7}$
  

• $\frac{x^7}{y}$
  

• x⁷y

Multiple Choice

Simplify:  $\left(s^2r^{-4}\right)\left(s^6r^{-2}\right)$  

•  $\frac{s^8}{r^6}$  

•  $\frac{s^{15}}{r^8}$  

•  $r^6s^8$  

•  $r^7s^{13}$  

Multiple Choice

Which expression is equivalent to  $\frac{x^2y^2z^2}{4y^4}$  ?

•  $4y^6$  

•  $y^6$  

•  $\frac{x^2z^2}{4y^2}$  

•  $4x^2y^6z^2$  

Refresher: Exponents and Radicals

SIMPLIFY RADICALS

know your perfect square factors:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225...

Refresher: Exponents and Radicals

RATIONALIZE DENOMINATOR:

This shows 2 ways to complete the same problem

Multiple Choice

 $\sqrt{36x^3y^4}$  

•  $6xy^2\sqrt{x}$  
  

•  $3y^2\sqrt{2x}$  
  

•  $3y\sqrt{x}$  

•  $6x\sqrt{3y}$  
  

Multiple Choice

 $\sqrt{28m^6}$  

•  $m^3\sqrt{7}$  
  

•  $7m^3\sqrt{2}$  
  

•  $2m^3\sqrt{7}$  
  

•  $2m^3\sqrt{7m^2}$  
  

Multiple Choice

Simplify:  $\sqrt{\frac{5}{2}}$  

•  $\sqrt{10}$  

•  $\frac{\sqrt{10}}{2}$  

•  $\frac{\sqrt{5}}{2}$  

•  $\sqrt{5}$  

Multiple Choice

Simplify:  $\frac{\sqrt{5}}{\sqrt{15}}$  

•  $\frac{\sqrt{3}}{3}$  

•  $\frac{5\sqrt{3}}{3}$  

•  $\frac{1}{3}$  

•  $\frac{\sqrt{5}}{3}$