Evaluate Using Scientific Notation (4*10^-5)^-6

${(4 \cdot 10^{- 5})}^{- 6}$

Step 1

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

$\frac{1}{{(4 \cdot 10^{- 5})}^{6}}$

Step 2

Simplify the denominator.

Apply the product rule to $4 \cdot 10^{- 5}$ .

$\frac{1}{4^{6} \cdot {(10^{- 5})}^{6}}$

Raise $4$ to the power of $6$ .

$\frac{1}{4096 \cdot {(10^{- 5})}^{6}}$

Multiply the exponents in ${(10^{- 5})}^{6}$ .

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

$\frac{1}{4096 \cdot 10^{- 5 \cdot 6}}$

Multiply $- 5$ by $6$ .

$\frac{1}{4096 \cdot 10^{- 30}}$

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

$\frac{1}{4096 \cdot \frac{1}{10^{30}}}$

Step 3

Combine $4096$ and $\frac{1}{10^{30}}$ .

$\frac{1}{\frac{4096}{10^{30}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{10^{30}}{4096}$

Step 5

Multiply $\frac{10^{30}}{4096}$ by $1$ .

$\frac{10^{30}}{4096}$