Evaluate 5^-3*(5^7)/(5^-7)

$5^{- 3} \cdot \frac{5^{7}}{5^{- 7}}$

Raise $5$ to the power of $7$ .

$5^{- 3} \cdot \frac{78125}{5^{- 7}}$

Simplify the denominator.

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

$5^{- 3} \cdot \frac{78125}{\frac{1}{5^{7}}}$

Raise $5$ to the power of $7$ .

$5^{- 3} \cdot \frac{78125}{\frac{1}{78125}}$

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

$\frac{1}{5^{3}} \cdot \frac{78125}{\frac{1}{78125}}$

Combine.

$\frac{1 \cdot 78125}{5^{3} \frac{1}{78125}}$

Multiply $78125$ by $1$ .

$\frac{78125}{5^{3} \frac{1}{78125}}$

Combine $5^{3}$ and $\frac{1}{78125}$ .

$\frac{78125}{\frac{5^{3}}{78125}}$

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

$\frac{78125}{\frac{125}{78125}}$

Cancel the common factor of $125$ and $78125$ .

Factor $125$ out of $125$ .

$\frac{78125}{\frac{125 (1)}{78125}}$

Cancel the common factors.

Factor $125$ out of $78125$ .

$\frac{78125}{\frac{125 \cdot 1}{125 \cdot 625}}$

Cancel the common factor.

$\frac{78125}{\frac{125 \cdot 1}{125 \cdot 625}}$

Rewrite the expression.

$\frac{78125}{\frac{1}{625}}$

Multiply the numerator by the reciprocal of the denominator.

$78125 \cdot 625$

Multiply $78125$ by $625$ .

$48828125$