Chapter 7.2, Problem 42PPS

To determine

To Simplify: The Given expression

  $\frac{g^0{h}^7{j}^{-2}}{g^{-5}{h}^0{j}^{-2}}$

Answer to Problem 42PPS

The simplified expression is. $g^5{h}^7$ .

Explanation of Solution

Given information:

  $\frac{g^0{h}^7{j}^{-2}}{g^{-5}{h}^0{j}^{-2}}$

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:

  $\frac{g^0{h}^7{j}^{-2}}{g^{-5}{h}^0{j}^{-2}}$

(Group the powers with the same base)

  $=\left(\frac{g^0}{g^{-5}}\right)\left(\frac{h^7}{h^0}\right)\left(\frac{j^{-2}}{j^{-2}}\right)$

Using Quotient of Powers

  $=g^{0-\left(-5\right)}{h}^{7-0}{j}^{-2-\left(-2\right)}$

Simplify.

  $=g^5{h}^7{j}^0$

Using Zero Exponent Property

  $=g^5{h}^7\cdot 1$

  $=g^5{h}^7$