Question

The value of ${\left(\frac{23}{25}\right)}^0\times {\left(\frac{-1}{2}\right)}^5\times 2^3\times {\left(\frac{3}{4}\right)}^2$ is _______.

• A. $-\frac{9}{64}$
• B. $\frac{9}{64}$
• C. $\frac{64}{9}$
• D. $-\frac{64}{9}$

Answer 1

The correct option is A $(-\frac{9}{64})$

Given ${\left(\frac{23}{25}\right)}^0\times {\left(\frac{-1}{2}\right)}^5\times 2^3\times {\left(\frac{3}{4}\right)}^2$

We know that $a^0=1$ and $(\frac{a}{b}{)}^m=\frac{a^m}{b^m}$

Thus it can be written as,
$1\times \frac{(-1{)}^5}{2^5}\times 8\times \frac{3^2}{4^2}$
$=1\times \left(\frac{-1}{32}\right)\times 8\times \left(\frac{9}{16}\right)$
$=-\frac{9}{64}$
Hence, the value of the given expression is $-\frac{9}{64}$