Question

The value of ${\left(256\right)}^{0.16}.{\left(256\right)}^{0.09}$ is:

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

Answer 1

The correct option is A $4$

we know,

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

and $256=4^4$

$\Rightarrow (256{)}^{0.16}\times (256{)}^{0.09}$ $=(256{)}^{0.25}$

we know,

$(a^m{)}^n=a^{mn}$

$\Rightarrow (4^4{)}^{0.25}$$=4^{4\times 0.25}$$=4^1=4$