Evaluate (1/((3.610^-4)^3))/(1/((610^3)^3))

$\frac{\frac{1}{{(3.6 \cdot 10^{- 4})}^{3}}}{\frac{1}{{(6 \cdot 10^{3})}^{3}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{{(3.6 \cdot 10^{- 4})}^{3}} {(6 \cdot 10^{3})}^{3}$

Step 2

Simplify the denominator.

Apply the product rule to $3.6 \cdot 10^{- 4}$ .

$\frac{1}{{3.6}^{3} \cdot {(10^{- 4})}^{3}} {(6 \cdot 10^{3})}^{3}$

Raise $3.6$ to the power of $3$ .

$\frac{1}{46.656 \cdot {(10^{- 4})}^{3}} {(6 \cdot 10^{3})}^{3}$

Multiply the exponents in ${(10^{- 4})}^{3}$ .

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

$\frac{1}{46.656 \cdot 10^{- 4 \cdot 3}} {(6 \cdot 10^{3})}^{3}$

Multiply $- 4$ by $3$ .

$\frac{1}{46.656 \cdot 10^{- 12}} {(6 \cdot 10^{3})}^{3}$

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

$\frac{1}{46.656 \cdot \frac{1}{10^{12}}} {(6 \cdot 10^{3})}^{3}$

Raise $10$ to the power of $12$ .

$\frac{1}{46.656 \cdot \frac{1}{1000000000000}} {(6 \cdot 10^{3})}^{3}$

Step 3

Combine $46.656$ and $\frac{1}{1000000000000}$ .

$\frac{1}{\frac{46.656}{1000000000000}} {(6 \cdot 10^{3})}^{3}$

Step 4

Divide $46.656$ by $1000000000000$ .

$\frac{1}{0} {(6 \cdot 10^{3})}^{3}$

Step 5

The expression contains a division by $0$ . The expression is undefined.

Undefined

Evaluate (1/((3.6*10^-4)^3))/(1/((6*10^3)^3))