Evaluate (1.25*10^-13)^-3

${(1.25 \cdot 10^{- 13})}^{- 3}$

Step 1

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

$\frac{1}{{(1.25 \cdot 10^{- 13})}^{3}}$

Step 2

Simplify the denominator.

Apply the product rule to $1.25 \cdot 10^{- 13}$ .

$\frac{1}{{1.25}^{3} \cdot {(10^{- 13})}^{3}}$

Raise $1.25$ to the power of $3$ .

$\frac{1}{1.953125 \cdot {(10^{- 13})}^{3}}$

Multiply the exponents in ${(10^{- 13})}^{3}$ .

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

$\frac{1}{1.953125 \cdot 10^{- 13 \cdot 3}}$

Multiply $- 13$ by $3$ .

$\frac{1}{1.953125 \cdot 10^{- 39}}$

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

$\frac{1}{1.953125 \cdot \frac{1}{10^{39}}}$

Step 3

Combine $1.953125$ and $\frac{1}{10^{39}}$ .

$\frac{1}{\frac{1.953125}{10^{39}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{10^{39}}{1.953125}$

Step 5

Multiply $\frac{10^{39}}{1.953125}$ by $1$ .

$\frac{10^{39}}{1.953125}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{10^{39}}{1.953125}$

Decimal Form:

$5.12 \cdot 10^{38}$