Question

In power notation, $\frac{81}{625}$ can be expressed as ___.

• A. $(\frac{3}{4}{)}^5$
• B. $(\frac{-3}{5}{)}^4$
• C. $(\frac{3}{5}{)}^4$
• D. $(\frac{5}{3}{)}^4$

Answer 1

Answer: (B), (C)

$(\frac{3}{5}{)}^4$

$81=3\times 3\times 3\times 3=3^4$

$625=5\times 5\times 5\times 5=5^4$

$\therefore \frac{81}{625}=\frac{3^4}{5^4}={\left(\frac{3}{5}\right)}^4$

${(-1)}^{evennumber}=+1$

Hence, ${\left(\frac{-3}{5}\right)}^4$ is also correct.