Evaluate 243^(-3/5)

$243^{\frac{- 3}{5}}$

Step 1

Move the negative in front of the fraction.

$243^{- \frac{3}{5}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{243^{\frac{3}{5}}}$

Step 3

Simplify the denominator.

Rewrite $243$ as $3^{5}$ .

$\frac{1}{{(3^{5})}^{\frac{3}{5}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{3^{5 (\frac{3}{5})}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{3^{5 (\frac{3}{5})}}$

Rewrite the expression.

$\frac{1}{3^{3}}$

Raise $3$ to the power of $3$ .

$\frac{1}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{27}$

Decimal Form:

$0.\overline{037}$