Chapter 7.2, Problem 3AGP

To determine

To Simplify: The Given expression

$\frac{b^4{c}^2{d}^0}{b^{2}c}$

Answer to Problem 3AGP

The simplified expression is $b^{2}c$ .

Explanation of Solution

Given information:

$\frac{b^4{c}^2{d}^0}{b^{2}c}$

Concept Used:

Power of a quotient: It states that in order to find the power of a quotient, find the power of the numerator and that of the denominator.

Example:let a and b be any non-zero number and m be any integer.

  $\frac{a^m}{b^m}=\frac{a^m}{b^m}$

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:

  $\frac{b^4{c}^2{d}^0}{b^{2}c}$

(Group the powers with the same base)

  $=\left(\frac{b^4}{b^2}\right)\left(\frac{c^2}{c}\right)d^0$

Using Quotient of Powers

  $=b^{4-2}{c}^{2-1}{d}^0$

Simplify.

  $=b^{2}c{d}^0$

Using Zero Exponent Property

  $=b^{2}c$