Question

Simplify ${\left( {\dfrac{5}{3}} \right)^{ - 3}}$

Answer 1

Hint: We will first try to eliminate the exponential term. We will use the property of exponent that is if a term has negative exponent, it reciprocates itself and its exponent become positive. Then, we will simply solve the exponents.

Complete answer:
We have to simplify ${\left( {\dfrac{5}{3}} \right)^{ - 3}}$
We will first distribute the exponential to the numerator and denominator.
$ = \left( {\dfrac{{{5^{ - 3}}}}{{{3^{ - 3}}}}} \right)$
We will reciprocate both numerator and denominator with each other because both have negative exponents.
$ = \left( {\dfrac{{{3^3}}}{{{5^3}}}} \right)$
We know that \[{3^3} = 27\] and \[{5^3} = 125\].
$ = \left( {\dfrac{{27}}{{125}}} \right)$
Hence, the polynomial ${\left( {\dfrac{5}{3}} \right)^{ - 3}}$ is equals to $\left( {\dfrac{{27}}{{125}}} \right)$

Note:
We will discuss the types of exponential questions. If the exponent is positive, we just multiply the base to itself the number of times indicated by the exponent/power. Any equation with the exponent 0 is equal to 1 and there is no need to consider the base value for simplification. Exponents that are rational or fractional will become radicals or roots. for example, ${3^{\dfrac{1}{3}}}$ may be expressed as $\sqrt 3 $ , whereas ${6^{\dfrac{5}{2}}}$ can be represented as 2 roots (or square root) of 6 raised to the power 5.