Evaluate (5^-1)/(5^-2)*5^-3

$\frac{5^{- 1}}{5^{- 2}} \cdot 5^{- 3}$

Step 1

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

$\frac{\frac{1}{5}}{5^{- 2}} \cdot 5^{- 3}$

Step 2

Simplify the denominator.

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

$\frac{\frac{1}{5}}{\frac{1}{5^{2}}} \cdot 5^{- 3}$

Raise $5$ to the power of $2$ .

$\frac{\frac{1}{5}}{\frac{1}{25}} \cdot 5^{- 3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{5} \cdot 25 \cdot 5^{- 3}$

Step 4

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

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

Cancel the common factor.

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

Rewrite the expression.

$5 \cdot 5^{- 3}$

Step 5

Multiply $5$ by $5^{- 3}$ by adding the exponents.

Multiply $5$ by $5^{- 3}$ .

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

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

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

$5^{1 - 3}$

Subtract $3$ from $1$ .

$5^{- 2}$

Step 6

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

$\frac{1}{5^{2}}$

Step 7

Raise $5$ to the power of $2$ .

$\frac{1}{25}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$