Simplify (4^5*3^5)^(-1/5)

${(4^{5} \cdot 3^{5})}^{- \frac{1}{5}}$

Step 1

Raise $4$ to the power of $5$ .

${(1024 \cdot 3^{5})}^{- \frac{1}{5}}$

Step 2

Raise $3$ to the power of $5$ .

${(1024 \cdot 243)}^{- \frac{1}{5}}$

Step 3

Multiply $1024$ by $243$ .

$248832^{- \frac{1}{5}}$

Step 4

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

$\frac{1}{248832^{\frac{1}{5}}}$

Step 5

Simplify the denominator.

Rewrite $248832$ as $12^{5}$ .

$\frac{1}{{(12^{5})}^{\frac{1}{5}}}$

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

$\frac{1}{12^{5 (\frac{1}{5})}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{12^{5 (\frac{1}{5})}}$

Rewrite the expression.

$\frac{1}{12^{1}}$

Evaluate the exponent.

$\frac{1}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{12}$

Decimal Form:

$0.08\overline{3}$