Evaluate (5^(4/5)*5^(4/5))^-10

${(5^{\frac{4}{5}} \cdot 5^{\frac{4}{5}})}^{- 10}$

Step 1

Multiply $5^{\frac{4}{5}}$ by $5^{\frac{4}{5}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(5^{\frac{4}{5} + \frac{4}{5}})}^{- 10}$

Combine the numerators over the common denominator.

${(5^{\frac{4 + 4}{5}})}^{- 10}$

Add $4$ and $4$ .

${(5^{\frac{8}{5}})}^{- 10}$

Step 2

Multiply the exponents in ${(5^{\frac{8}{5}})}^{- 10}$ .

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

$5^{\frac{8}{5} \cdot - 10}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

$5^{\frac{8}{5} \cdot (5 (- 2))}$

Cancel the common factor.

$5^{\frac{8}{5} \cdot (5 \cdot - 2)}$

Rewrite the expression.

$5^{8 \cdot - 2}$

Multiply $8$ by $- 2$ .

$5^{- 16}$

Step 3

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

$\frac{1}{5^{16}}$

Step 4

Raise $5$ to the power of $16$ .

$\frac{1}{152587890625}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{152587890625}$

Decimal Form:

$6.5536 \cdot 10^{- 12}$