9-4 Practice

The volume of a rectangular prism is  $6x^4y^3$  cubic inches.  The length is  $2xy$  inches. The width is  $3x$  inches.  Which expression represents the height?

•  $36x^6y^4$  

•  $x^2y^2$  

•  $x^3y^3$  

•  $36x^4y^3$  

The length of a rectangle is  $10m^8n^6$  yards.  The width is  $5m^5n^5$  yards.  Which expression represents the area of the rectangle?

•  $50m^{13}n^{11}$  

•  $2m^3n$  

•  $5m^3n$  

•  $15m^{13}n^{11}$  

The expression  $\left(12p^{15}\right)\left(-3p^4\right)$  is equivalent to  $c\cdot p^{19}.$  

What is the value of  $c?$  

The expression  $\left(-2x^9\right)\left(x^{-15}\right)$  is equivalent to  $-2x^c.$  

What is the value of  $c?$  

Which expression is equivalent to  $\left(243v^{25}w^{15}\right)^{\frac{1}{5}}?$  

•  $81v^{25}w^{15}$  

•  $1215v^{125}w^{75}$  

•  $\frac{243}{5}v^5w^3$  

•  $3v^5w^3$  

The expression  $\frac{\left(m^7\right)^{-4}}{m^{-35}}$  is equivalent to  $m^c.$  

What is the value of  $c?$  

Which expression is equivalent to the expression below?

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

•  $\frac{3y^6}{2x^4}$  

•  $18x^4y^6$  

•  $\frac{18y^6}{x^4}$  

•  $\frac{18y^5}{x^3}$  

Which expression is equivalent to the expression below?

 $\frac{9x^0y^{-3}z^{10}}{36x^9y^{-13}z^{-2}}$  

•  $\frac{4y^{10}z^{12}}{x^9}$  

•  $\frac{y^{10}z^{12}}{4x^9}$  

•  $\frac{y^{10}z^{12}}{27x^8}$  

•  $\frac{y^{10}z^{20}}{4x^8}$  

The expression  $\left(-4w^3\right)^4$  is equivalent to  $c\cdot w^{12}.$  

What is the value of  $c?$  

The expression  $\left(-3x^{13}\right)\left(x^9\right)^5$  is equivalent to  $-3x^c.$  

What is the value of  $c?$