Question

How do you simplify $5{x^{ - 4}}$ with positive exponents?

Answer 1

Hint:We are going to find which coefficient has the negative exponent, then we know that when we shift a variable with the negative exponent to be shifted to the other side it becomes a positive exponent. So, we are going to send the $x$with the negative exponent to the denominator such that we get it converted to a positive exponent and hence, we have got the given terms in the positive exponent. By using one of the laws \[{x^{ - m}} = \dfrac{1}{{{x^m}}}\],we can convert the negative exponent to the positive exponent expression.

Complete step by step answer:
We are given $5{x^{ - 4}}$, from which we can identify that the negative exponent is just associated to $x$,
So just we need to transform only it and not the whole term.
So, using this one of the laws of indices states: \[{x^{ - m}} = \dfrac{1}{{{x^m}}}\],
Coming to the clarity of the given problem
\[5{x^{ - 4}} = 5 \cdot {x^{ - 4}}\]
We can see it from that the negative exponent is just to the $x$and not to the constant $5$
We can write the given as
$5{x^{ - 4}} = \dfrac{5}{{{x^4}}}$
If in other case, it was like \[{(5x)^{ - 4}}\], then we represent it as this way
\[{(5x)^{ - 4}} = \dfrac{1}{{{{(5x)}^4}}}\]

Thus upon simplification of $5{x^{ - 4}}$, we get $\dfrac{1}{{{{(5x)}^4}}}$ as the positive exponent.

Note:We have to be careful in identifying whether the given negative exponents are belonging to the whole terms or else just one of the terms. When we are going to transform, if the negative exponent is on the whole term, then transform whole terms and just not only by sending the power to the denominator/numerator according to the question.