Evaluate 1/( cube root of 9.9*10^14)

$\frac{1}{\sqrt[3]{9.9 \cdot 10^{14}}}$

Step 1

Rewrite $9.9 \cdot 10^{14}$ as $0.99 \cdot 10^{15}$ .

$\frac{1}{\sqrt[3]{0.99 \cdot 10^{15}}}$

Step 2

Rewrite $\sqrt[3]{0.99 \cdot 10^{15}}$ as $\sqrt[3]{0.99} \cdot \sqrt[3]{10^{15}}$ .

$\frac{1}{\sqrt[3]{0.99} \cdot \sqrt[3]{10^{15}}}$

Step 3

Evaluate the root.

$\frac{1}{0.99665549 \cdot \sqrt[3]{10^{15}}}$

Step 4

Rewrite $10^{15}$ as ${(10^{5})}^{3}$ .

$\frac{1}{0.99665549 \cdot \sqrt[3]{{(10^{5})}^{3}}}$

Step 5

Pull terms out from under the radical, assuming real numbers.

$\frac{1}{0.99665549 \cdot 10^{5}}$

Step 6

Divide using scientific notation.

Group coefficients together and exponents together to divide numbers in scientific notation.

$(\frac{1}{0.99665549}) (\frac{1}{10^{5}})$

Divide $1$ by $0.99665549$ .

$1.00335572 \frac{1}{10^{5}}$

Move $10^{5}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$1.00335572 \cdot 10^{- 5}$