Mixed Exponent Rules

Simplify:  $\left(3x^2y^3\right)\left(2xy^3\right)$  

•  $6x^3y^6$  

•  $6x^2y^6$  

•  $3x^3y^5$  

•  $1$  

Answer explanation

3(2)= 6
 $x^2\left(x^1\right)\ =\ x^3$  

 $y^3\left(y^3\right)=\ y^6$  

Tags

CCSS.HSA.APR.A.1

Simplify:  $\frac{24x^4y^2z^3}{32y^2xz^6}$  

•  $\frac{3x^3}{4z^3}$  

•  $\frac{24x^3}{32z^3}$  

•  $\frac{8x^3}{16z^3}$  

•  $\frac{2x^3}{3z^3}$  

Answer explanation

 $\frac{24}{32}=\frac{3}{4}\ \ \ Divide\ both\ by\ 8$  
 $\frac{x^4}{x^1}=x^3$  
 $\frac{y^2}{y^2}=y^0=1$  
 $\frac{z^3}{z^6}=z^{-3}=\frac{1}{z^3}$  

Tags

CCSS.HSA.APR.A.1

Simplify the following expression:

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Answer explanation

When you one base but 2 exponents, you multiply the exponents.

Tags

CCSS.HSA.APR.A.1

 $Simplify:\ \left(-3x^3y^{22}\right)^0$  

•  $1$  

•  $-3$  

•  $3$  

•  $-3x^3y^2$  

Answer explanation

Anything to the bother of none is 1!

Tags

CCSS.HSA.SSE.A.2

Simplify:  $\frac{4x^{-4}y^2}{8x^{-6}y^{-2}}$  

•  $\frac{x^2y^4}{2}$  

•  $\frac{2x^2}{y^4}$  

•  $2x^2y^4$  

•  $\frac{1}{2x^6}$  

Answer explanation

 $\frac{4}{8\ }=\ \frac{1}{2}\ Both\ numbers\ are\ divisible\ by\ 4.$   $\frac{x^{-4}}{x^{-6}}=\ x^2$  
 $\frac{y^2}{y^{-2}}=\ y^4$  

Tags

CCSS.HSA.APR.A.1

Simplify:  $\frac{20x^9y^7}{5x^2y^9}$  

•  $\frac{4x^7}{y^2}$  

•  $4x^7y^2$  

•  $4x^{11}y^{16}$  

•  $4x^{4.5}y^{.77}$  

Answer explanation

 $\frac{20}{5}=4\$  
 $\frac{x^9}{x^2}=x^7$  

 $\frac{y^7}{y^9}=y^{-2}=\frac{1}{y^2}$  

Tags

CCSS.HSA.APR.A.1

(2m⁴)(5m²)

• 10m⁶

• 10m⁸

• 7m⁶

• 7m⁸

Answer explanation

2(5) = 10
$m^4\left(m^2\right)=m^6$

Tags

CCSS.HSA.APR.A.1

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Tags

CCSS.8.EE.A.1

Simplify

x⁻⁶

• 1 ⁄ x⁶

• x⁶

• -x⁶

• -1 ⁄ x⁶

Answer explanation

Negative exponent means wrong place. When you put it in the write place, change the exponent to positive.

Tags

CCSS.HSN.RN.A.2

(2ab)³

• 2³a³b³

• 2ab³

• 6a³b³

• 6ab

Answer explanation

Everything inside the parenthesis is cubed (raised to the 3rd power).
$2^3=8$

$\left(a^1\right)^3=a^3$

$\left(b^1\right)^3=b^3$

Tags

CCSS.6.EE.A.1

CCSS.6.EE.A.2

CCSS.6.EE.A.3

CCSS.6.EE.A.4