Algebra Examples

$2^{- 3} \cdot 5^{- 2} \cdot 7^{0}$

Step 1

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

$\frac{1}{2^{3}} \cdot 5^{- 2} \cdot 7^{0}$

Step 2

Raise $2$ to the power of $3$ .

$\frac{1}{8} \cdot 5^{- 2} \cdot 7^{0}$

Step 3

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

$\frac{1}{8} \cdot \frac{1}{5^{2}} \cdot 7^{0}$

Step 4

Combine.

$\frac{1 \cdot 1}{8 \cdot 5^{2}} \cdot 7^{0}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $1$ by $1$ .

$\frac{1}{8 \cdot 5^{2}} \cdot 7^{0}$

Step 5.2

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

$\frac{1}{8 \cdot 25} \cdot 7^{0}$

Step 5.3

Multiply $8$ by $25$ .

$\frac{1}{200} \cdot 7^{0}$

Step 5.4

Anything raised to $0$ is $1$ .

$\frac{1}{200} \cdot 1$

Step 5.5

Multiply $\frac{1}{200}$ by $1$ .

$\frac{1}{200}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{200}$

Decimal Form:

$0.005$