Question

Simplify $(0.00032{)}^{\frac{4}{5}}.$

• A. $0.0016$
• B. $0.0008$
• C. $0.00016$
• D. $0.00008$

Answer 1

The correct option is A $0.0016$

$\underset{–}{\text{Need to Simplify:}}$ $(0.00032{)}^{\frac{4}{5}}$

$(0.00032{)}^{\frac{4}{5}}=(32\times {10}^{-5}{)}^{\frac{4}{5}}$

[As the decimal point is moved $5$ places to right]

$=(\frac{32}{{10}^5}{)}^{\frac{4}{5}}$ $[\because a^{-n}=\frac{1}{a^n}]$

$=(\frac{2^5}{{10}^5}{)}^{\frac{4}{5}}$ $[\because 32=2\times 2\times 2\times 2\times 2=2^5]$

$=((\frac{2}{10}{)}^5{)}^{\frac{4}{5}}$ $[\because \frac{a^n}{b^n}=(\frac{a}{b}{)}^n]$

$=(\frac{2}{10}{)}^{5\times \frac{4}{5}}$ $[\because (a^m{)}^n=a^{m\times n}]$

$=(\frac{2}{10}{)}^4=(0.2{)}^4$

$=0.2\times 0.2\times 0.2\times 0.2$

$\Rightarrow \underset{–}{(0.00032{)}^{\frac{4}{5}}=0.0016}$

Hence, the value of $(0.00032{)}^{\frac{4}{5}}$ is equal to $0.0016$ .

Therefore, option (a.) is the correct answer.