Finite Math Examples

${(2.5 \cdot 10^{- 18})}^{- 3}$

Step 1

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

$\frac{1}{{(2.5 \cdot 10^{- 18})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2.5 \cdot 10^{- 18}$ .

$\frac{1}{{2.5}^{3} \cdot {(10^{- 18})}^{3}}$

Step 2.2

Raise $2.5$ to the power of $3$ .

$\frac{1}{15.625 \cdot {(10^{- 18})}^{3}}$

Step 2.3

Multiply the exponents in ${(10^{- 18})}^{3}$ .

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Step 2.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{15.625 \cdot 10^{- 18 \cdot 3}}$

Step 2.3.2

Multiply $- 18$ by $3$ .

$\frac{1}{15.625 \cdot 10^{- 54}}$

Step 2.4

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

$\frac{1}{15.625 \cdot \frac{1}{10^{54}}}$

Step 3

Combine $15.625$ and $\frac{1}{10^{54}}$ .

$\frac{1}{\frac{15.625}{10^{54}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{10^{54}}{15.625}$

Step 5

Multiply $\frac{10^{54}}{15.625}$ by $1$ .

$\frac{10^{54}}{15.625}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{10^{54}}{15.625}$

Decimal Form:

$6.4 \cdot 10^{52}$