Finite Math Examples

$((7^{- 9}) (5^{- 3})) \cdot 10$

Step 1

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

$\frac{1}{7^{9}} \cdot 5^{- 3} \cdot 10$

Step 2

Raise $7$ to the power of $9$ .

$\frac{1}{40353607} \cdot 5^{- 3} \cdot 10$

Step 3

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

$\frac{1}{40353607} \cdot \frac{1}{5^{3}} \cdot 10$

Step 4

Combine.

$\frac{1 \cdot 1}{40353607 \cdot 5^{3}} \cdot 10$

Step 5

Simplify the expression.

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Step 5.1

Multiply $1$ by $1$ .

$\frac{1}{40353607 \cdot 5^{3}} \cdot 10$

Step 5.2

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

$\frac{1}{40353607 \cdot 125} \cdot 10$

Step 5.3

Multiply $40353607$ by $125$ .

$\frac{1}{5044200875} \cdot 10$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $5044200875$ .

$\frac{1}{5 (1008840175)} \cdot 10$

Step 6.2

Factor $5$ out of $10$ .

$\frac{1}{5 \cdot 1008840175} \cdot (5 \cdot 2)$

Step 6.3

Cancel the common factor.

$\frac{1}{5 \cdot 1008840175} \cdot (5 \cdot 2)$

Step 6.4

Rewrite the expression.

$\frac{1}{1008840175} \cdot 2$

Step 7

Combine $\frac{1}{1008840175}$ and $2$ .

$\frac{2}{1008840175}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{1008840175}$

Decimal Form:

$1.98247457 \cdot 10^{- 9}$