Question

How do you simplify $8{{x}^{-3}}{{y}^{3}}$ and write it using only positive exponents?

Answer 1

Hint: In this question we have been asked to simplify the given expression $8{{x}^{-3}}{{y}^{3}}$ using positive exponents only. For doing that we will initially simplify the given expression by performing simple basic arithmetic calculations and then reduce it in a form consisting of positive exponents only. As we know that eight can be written as two raised to power of three we will use this and write the expression simply as $8{{x}^{-3}}{{y}^{3}}={{2}^{3}}{{x}^{-3}}{{y}^{3}}$ and further simplify it.

Complete step by step solution:
Here in this we need to simplify the given expression $8{{x}^{-3}}{{y}^{3}}$ in terms of positive exponents only.
For that sake we will perform some simple arithmetic basic calculations and do that.
Initially we can use our knowledge and express the number eight in the expression as two to the power of three.
This can be mathematically expressed as $\Rightarrow 8{{x}^{-3}}{{y}^{3}}={{2}^{3}}{{x}^{-3}}{{y}^{3}}$ .
Now we will take the number three as common which is present in the exponent of ever number in the expression and simply express this expression mathematically as $\Rightarrow {{2}^{3}}{{x}^{-3}}{{y}^{3}}={{\left( 2y{{x}^{-1}} \right)}^{3}}$ .
Now as in the question it is mentioned to express in terms of positive exponents only we will shift the variable $x$ from numerator to denominator after doing this we will have $\Rightarrow {{\left( 2y{{x}^{-1}} \right)}^{3}}={{\left( \dfrac{2y}{x} \right)}^{3}}$ .
Therefore we can conclude that the given expression $8{{x}^{-3}}{{y}^{3}}$ can be simply expressed only in terms of positive exponents as $8{{x}^{-3}}{{y}^{3}}={{\left( \dfrac{2y}{x} \right)}^{3}}$ .

Note: While answering questions of this type very few mistakes are possible and a few numbers of steps are involved so they are less time consuming. Therefore we should be sure with our concepts and the calculations we make during the solution. Similarly we can simplify and express any expression for example $27{{m}^{-3}}{{p}^{3}}={{3}^{3}}{{m}^{-3}}{{p}^{3}}={{\left( 3p{{m}^{-1}} \right)}^{3}}={{\left( \dfrac{3p}{m} \right)}^{3}}$ .