Unit 8 Review

A rectangular prism has a width of $$x^3y$$  inches, a length of $$x$$ inches, and a height of $$y^4$$ inches.  Which expression represents the volume in cubic inches of this rectangular prism?

The area of a rectangle is $$42x^6y^5$$ square yards.  If the length of the rectangle is $$7x^4y$$ yards, which expression represents the width of the rectangle in yards?

Which expression equivalent to  $$\left(xy^{-7}\right)^3$$  

for all values of $$x$$  and $$y$$  where the expression is defined?

The expression  $\left(x^2\right)\left(x^{-10}\right)$  is equivalent to  $x^n.$  What is the value of  $n?$  

(a)  

Which expression equivalent to  $\left(121x^4y^{16}\right)^{\frac{1}{2}}?$  

Which expression equivalent to  $\frac{\left(q^4\right)^{-5}}{q^{-25}}$   for all values of  $q$  where the expression is defined?

Which expression is equivalent to  $\frac{12q^7w^8}{2w^3}\cdot\frac{3\left(q^4\right)^2}{w^{-6}}$  for all values of  $q$  and  $w$  where the  expression is defined?

Which expression is equivalent to  $\frac{50m^{-4}p^3v^9}{10m^{-2}p^5v^{-6}}$  for all values of  $m,\ p,\$ and  $v$  where the expression is defined?

Which expression is equivalent to $$\left(4x^{11}y\right)^3?$$    

The expression $\left(x^{25}\right)\left(x^{10}\right)^3$  is equivalent to  $x^p.$    

What is the value of  $p?$  

(a)