Q. 109 - Intermediate Algebra

Question

(a)$b^4{b}^{-8}$

(b)$\left(w^4{x}^{-5}\right)\left(w^{-2}{x}^{-4}\right)$

(c)$(-6c^{-3}{d}^9)\left(2c^4{d}^{-5}\right)$

Step-by-Step Solution

Answer

(a) $b^{-4}$

(b)$w^2{x}^{-9}$

(c)$-12c{d}^4$

Part (a) Step 1 . Given Information

The given expression is :

$b^4{b}^{-8}$, we need to simplify the expression.

Part (a) Step 2 . Product Property

If$a$is a real number and $m$ and $n$ are integers, then :

$a^m.a^n=a^{m+n}$

Part (a) Step 3 . Simplify the expression

By using the Product Property :

$b^4{b}^{-8}=b^{4+(-8)}$

  $b^{4-8}=b^{-4}$

Part (b) Step 1 . Given Information

The given expression is :$\left(w^4{x}^{-5}\right)\left(w^{-2}{x}^{-4}\right)$, we need to simplify the expression.

Part (b) Step 2 . Product Property

If $a$ is real number and $m$ and $n$ are integers, then :

$a^m.a^n=a^{m+n}$

Part (b) Step 3 . Simplify the expression

By using the Product Property :

$\left(w^4{x}^{-5}\right)\left(w^{-2}{x}^{-4}\right)=w^{4+(-2)}{x}^{-5+(-4)}$

         $w^{4-2}{x}^{-5-4}=w^2{x}^{-9}$
 

Part (c) Step 1 . Given Information

The given expression is :

$(-6c^{-3}{d}^9)\left(2c^4{d}^{-5}\right)$ , we need to simplify the expression.

Part (c) Step 2 . Product Property

If $a$ is a real number and $m$ and $n$are integers, then :

$a^m.a^n=a^{m+n}$

Part (c) Step 3 . Simplify the expression

 By using the Product Property :

$(-6c^{-3}{d}^9)\left(2c^4{d}^{-5}\right)= (-6.2c^{-3+4})\left(d^{9+(-5)}\right)$

              $-12c^1{d}^{9-5}=-12c{d}^4$