Question

The value of ${\left(-\frac{1}{2}\right)}^{-5}$ is:

• A. $1$
• B. $-2$
• C. $-32$
• D. $32$

Answer 1

The correct option is C

$-32$

Finding the value of ${\left(-\frac{1}{2}\right)}^{-5}$

${\left(-\frac{1}{2}\right)}^{-5}=\frac{{\left(-1\right)}^{-5}}{{\left(2\right)}^{-5}}$

$\frac{{\left(-1\right)}^{-5}}{{\left(2\right)}^{-5}}=\frac{{\left(2\right)}^5}{{\left(-1\right)}^5}$

$\frac{{\left(2\right)}^5}{{\left(-1\right)}^5}=\frac{2\times 2\times 2\times 2\times 2}{\left(-1\right)}$

$\frac{2\times 2\times 2\times 2\times 2}{\left(-1\right)}=-32$

Hence, option (c) i.e. $-32$ is correct.