Question

$(4{)}^{0.5}\times (0.5{)}^4$ is

Answer 1

The given expression is $(4{)}^{0.5}\times (0.5{)}^4$

We can write $4=2^2$ and $0.5=\frac{1}{2}$

Hence, we will have,

$(2^2{)}^{0.5}\times {\left(\frac{1}{2}\right)}^4$

We know that, $(a^m{)}^n=a^{m\times n}$ and ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

Hence, we can further simplify the expression as,

$(2{)}^{2\times 0.5}\times \frac{1^4}{2^4}$

$\Rightarrow (2{)}^1\times \frac{1^4}{2^4}$

We also know that, $\frac{1}{a^m}=a^{-m}$

Hence, $2^1\times 2^{-4}$

Also, $a^m\times a^n=a^{m+n}$

Hence, $2^{1-4}=2^{-3}$

$\Rightarrow 2^{-3}=\frac{1}{2^3}$

$\Rightarrow \frac{1}{8}[2^3=2\times 2\times 2=8]$

$\Rightarrow \frac{1}{8}=0.125$

Hence, $(4{)}^{0.5}\times (0.5{)}^4=0.125$