Question

In power notation, $\frac{81}{16}$ can be expressed as ___.

• A. $\left(\frac{3^4}{2^4}\right)$
• B. $(\frac{3}{4}{)}^3$
• C. $(\frac{3}{2}{)}^4$
• D. $(\frac{3}{2}{)}^3$

Answer 1

Answer: (A), (C)

The correct options are
A

$\left(\frac{3^4}{2^4}\right)$

C

$(\frac{3}{2}{)}^4$

We can write:
$81=3\times 3\times 3\times 3$
$16=2\times 2\times 2\times 2$

So, $\frac{81}{16}$ = $\left(\frac{3^4}{2^4}\right)$

And we know that, $\left(\frac{a^m}{b^m}\right)=(\frac{a}{b}{)}^m$
$\therefore \frac{81}{16}$ = $\left(\frac{3^4}{2^4}\right)$ $=(\frac{3}{2}{)}^4$