Question

The simplified form of $(256{)}^{0.16}\times (256{)}^{0.09}$ is:

• A. $4$
• B. $16$
• C. $64$
• D. $256.25$

Answer 1

The correct option is A $4$

We can use one of the laws of exponent

$a^m.a^n=a^{m+n}$.
${\left(256\right)}^{0.16}\times {\left(256\right)}^{0.09}={\left(256\right)}^{\frac{16}{100}}\times {\left(256\right)}^{\frac{9}{100}}={\left(256\right)}^{(\frac{16}{100}+\frac{9}{100})}={\left(256\right)}^{\frac{25}{100}}={\left(256\right)}^{\frac{1}{4}}=\sqrt[4]{4256}=4$

Hence, option A is correct answer.