Basic Math Examples

${(9 \cdot 10^{2})}^{- 3}$

Step 1

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

$\frac{1}{{(9 \cdot 10^{2})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $9 \cdot 10^{2}$ .

$\frac{1}{9^{3} \cdot {(10^{2})}^{3}}$

Step 2.2

Raise $9$ to the power of $3$ .

$\frac{1}{729 \cdot {(10^{2})}^{3}}$

Step 2.3

Multiply the exponents in ${(10^{2})}^{3}$ .

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Step 2.3.1

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

$\frac{1}{729 \cdot 10^{2 \cdot 3}}$

Step 2.3.2

Multiply $2$ by $3$ .

$\frac{1}{729 \cdot 10^{6}}$

Step 2.4

Raise $10$ to the power of $6$ .

$\frac{1}{729 \cdot 1000000}$

Step 3

Multiply $729$ by $1000000$ .

$\frac{1}{729000000}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{729000000}$

Decimal Form:

$1.37174211 \cdot 10^{- 9}$