Question

Evaluate the expression $18-{\left(\sqrt[3]{27}\right)}^3$.

Answer 1

Given expression: $18-{\left(\sqrt[3]{27}\right)}^3$.

We know that

$\sqrt[\mathrm{n}]{\mathrm{a}}={\left(\mathrm{a}\right)}^{\frac{1}{\mathrm{n}}}\&{\left\{{\left(\mathrm{a}\right)}^{\mathrm{m}}\right\}}^{\mathrm{n}}={\left(\mathrm{a}\right)}^{\mathrm{m}\times \mathrm{n}}$

Now,

$18-{\left(\sqrt[3]{27}\right)}^3$

$=18-{\left\{{\left(27\right)}^{\frac{1}{3}}\right\}}^3$

$$\begin{gathered} =18-{\left(27\right)}^{\frac{1}{3}\times 3} \\ =18-27 \\ =-9 \end{gathered}$$

Hence, $18-{\left(\sqrt[3]{27}\right)}^3=-9$.