Algebra Examples

$5^{0} \cdot 5^{- 1} \cdot 5^{- 2}$

Step 1

Multiply $5^{0}$ by $5^{- 1}$ by adding the exponents.

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Step 1.1

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

$5^{0 - 1} \cdot 5^{- 2}$

Step 1.2

Subtract $1$ from $0$ .

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

Step 2

Multiply $5^{- 1}$ by $5^{- 2}$ by adding the exponents.

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Step 2.1

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

$5^{- 1 - 2}$

Step 2.2

Subtract $2$ from $- 1$ .

$5^{- 3}$

Step 3

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

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

Step 4

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

$\frac{1}{125}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{125}$

Decimal Form:

$0.008$