Q. 112 - Intermediate Algebra

Question

(a)$y^5{y}^{-5}$

(b)$\left(p{q}^{-4}\right)\left(p^{-6}{q}^{-3}\right)$

(c)$(-5m^4{n}^6)\left(8m^{-5}{n}^{-3}\right)$

Step-by-Step Solution

Answer

(a)$1$

(b)$p^{-5}{q}^{-7}$

(c)$-40m^{-1}{n}^3$

Part (a) Step 1 . Given Information

We are given the expression :

$y^5{y}^{-5}$, we need to simplify the expression

Part (a) Step 2 . Product Property and Zero Exponent property

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

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

       $a^0=1$

Part (a) Step 3 . Simplify the expression

Using the product property :

$y^5{y}^{-5}=y^{5+(-5)}$

  $y^{5-5}=y^0$

      $y^0=1$ (zero exponent property)

Part (b) Step 1 . Given Information

We are given the expression :

$\left(p{q}^4\right)\left(p^{-6}{q}^{-3}\right)$, we need to simplify the expression

Part (b) 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 (b) Step 3 . Simplify the expression

Using the Product Property :

$\left(p{q}^{-4}\right)\left(p^{-6}{q}^{-3}\right)=p^{1+(-6)}{q}^{-4+(-3)}$

       $p^{1-6}{q}^{-4-3}=p^{-5}{q}^{-7}$

Part (c) Step 1 . Given Information

We are given the expression :

$(-5m^4{n}^6)\left(8m^{-5}{n}^{-3}\right)$, 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

Using the Product Property :

$(-5m^4{n}^6)\left(8m^{-5}{n}^{-3}\right)=(-5.8m^{4+(-5)})\left(n^{6+(-3)}\right)$

                                                               $-40m^{4-5}{n}^{6-3}=-40m^{-1}{n}^3$