Question

(a)$s^3{s}^{-7}$

(b)$\left(m^3{n}^{-3}\right)\left(m^{-5}{n}^{-1}\right)$

(c)$(-2j^{-5}{k}^8)\left(7j^2{k}^{-3}\right)$

Short answer

(a)$s^{-4}$

(b)$m^{-2}{n}^{-4}$

(c)$-14j^{-3}{k}^5$

Step-by-step solution

Part (a) Step 1 . Given Information

The given expression is :

$s^3{s}^{-7}$, 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

Using the Product property :

$s^3{s}^{-7}=s^{3+(-7)}$

$s^{3-7}=s^4$

Part (b) Step 1 . Given Information

The given expression is :

$\left(m^3{n}^{-3}\right)\left(m^{-5}{n}^{-1}\right)$, we need to simplify the expression

Part (b) Step 2 . Product Property

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

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

Part (b) Step 3 .Simplify the expression

Using the Product Property :

$\left(m^3{n}^{-3}\right)\left(m^{-5}{n}^{-1}\right)=m^{3+(-5)}{n}^{-3+(-1)}$

$m^{3-5}{n}^{-3-1}=m^{-2}{n}^{-4}$

Part (c) Step 1 . Given Information

The given expression is :

$(-2j^{-5}{k}^8)\left(7j^3{k}^{-3}\right)$, 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 :

$(-2j^{-5}{k}^8)\left(7j^2{k}^{-3}\right)=(-2.7j^{-5+2})\left(k^{8+-\left(3\right)}\right)$

$-14j^{-3}{k}^{8-3}=-14j^{-3}{k}^5$