Evaluate ((5^-2)/5)^4

${(\frac{5^{- 2}}{5})}^{4}$

Step 1

Move $5^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{5 \cdot 5^{2}})}^{4}$

Step 2

Multiply $5$ by $5^{2}$ by adding the exponents.

Multiply $5$ by $5^{2}$ .

Raise $5$ to the power of $1$ .

${(\frac{1}{5^{1} \cdot 5^{2}})}^{4}$

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

${(\frac{1}{5^{1 + 2}})}^{4}$

Add $1$ and $2$ .

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

Step 3

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

${(\frac{1}{125})}^{4}$

Step 4

Apply the product rule to $\frac{1}{125}$ .

$\frac{1^{4}}{125^{4}}$

Step 5

One to any power is one.

$\frac{1}{125^{4}}$

Step 6

Raise $125$ to the power of $4$ .

$\frac{1}{244140625}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{244140625}$

Decimal Form:

$4.096 \cdot 10^{- 9}$