Algebra Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

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

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

Step 4

Combine.

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

Step 5

Multiply $78125$ by $1$ .

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

Step 6

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

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

Step 7

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

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

Step 8

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

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Step 8.1

Factor $125$ out of $125$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $125$ out of $78125$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

Multiply the numerator by the reciprocal of the denominator.

$78125 \cdot 625$

Step 10

Multiply $78125$ by $625$ .

$48828125$