Chapter 7.2, Problem 39PPS

To determine

To Simplify: The Given expression

  $\frac{39t^{4}u{v}^{-2}}{13t^{-3}{u}^7}$

Answer to Problem 39PPS

The simplified expression is

Explanation of Solution

Given information:

  $\frac{39t^{4}u{v}^{-2}}{13t^{-3}{u}^7}$

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.

  $\frac{a^m}{a^n}=a^{m-n}$

Negative Exponent Property: $a^{-n}$ is the reciprocal of $a^n$ , where a is a non-zero number and n is an integer.

  $a^{-n}=\frac{1}{a^n}$

Calculation:

  $\frac{39t^{4}u{v}^{-2}}{13t^{-3}{u}^7}$

(Group the powers with the same base)

  $=\left(\frac{39}{13}\right)\left(\frac{t^4}{t^{-3}}\right)\left(\frac{u}{u^7}\right)v^{-2}$

Using Quotient of Powers

  $=\left(\frac{39}{13}\right)t^{4-\left(-3\right)}{u}^{1-7}{v}^{-2}$

Simplify.

  $=\left(\frac{39}{13}\right)t^7{u}^{-6}{v}^{-2}$

Using Negative Exponent Property

  $=\left(\frac{39}{13}\right)t^7\left(\frac{1}{u^6}\right)\left(\frac{1}{v^2}\right)$

Simplify

  $=\frac{3t^7}{u^6{v}^2}$