Chapter 7.2, Problem 14CYU

To determine

To Simplify: The Given expression

$\frac{4r^2{v}^0{t}^5}{2r{t}^3}$

Answer to Problem 14CYU

The simplified expression is $2r{t}^2$ .

Explanation of Solution

Given information:

$\frac{4r^2{v}^0{t}^5}{2r{t}^3}$

Concept Used:

Quotient of powers: It states that to divide two powers with same base, subtract the exponent.

For example, let a be any non-zero number and m and n be any integer.

  $\frac{a^m}{a^n}=a^{m-n}$

Zero Exponent Property:Any non-zero number raised to the power zero is 1.

Example:let a be any non-zero number

  $a^0=1$

Calculation:

  $\frac{4r^2{v}^0{t}^5}{2r{t}^3}$

(Group the powers with the same base)

  $=\left(\frac{4}{2}\right)\left(\frac{r^2}{r}\right)\left(\frac{t^5}{t^3}\right)v^0$

Using Quotient of Powers

  $=\left(\frac{4}{2}\right)r^{2-1}{t}^{5-3}{v}^0$

Simplify.

  $=2r^1{t}^2{v}^0$

Applying Zero Exponent Property.

  $\begin{array}{l}=2r{t}^2\cdot 1\\ =2r{t}^2\end{array}$