Question

If $a=(-2)$, then find the value of ${\left(2a\right)}^5\times {\left(\frac{a}{2}\right)}^3÷(a{)}^4$

• A. $54$
• B. $64$
• C. $70$
• D. None of these

Answer 1

The correct option is B $64$

We have,

$a=(-2)$

We have to find the value of

${\left(2a\right)}^5\times {\left(\frac{a}{2}\right)}^3÷{\left(a\right)}^4$

On putting the value of $a=-2$ we get,

$={\left(2\times -2\right)}^5\times {\left(\frac{-2}{2}\right)}^3÷{\left(-2\right)}^4$

$={\left(-4\right)}^5\times {\left(-1\right)}^3÷{\left(-2\right)}^4$

$=\frac{-4\times -4\times -4\times -4\times -4\times -1\times -1\times -1}{-2\times -2\times -2\times -2}$

$=\frac{-4\times -4\times -4\times -4\times -4\times -1\times -1\times -1}{-2\times -2\times -2\times -2}$

$=\frac{4\times 4\times 4\times 4\times 4}{2\times 2\times 2\times 2}\left[weknowthat(-)\times (-)=(+)\right]$

$=4\times 2\times 2\times 2\times 2\left[divide4by2weget2\right]$

$=64$