Algebra Examples

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

Step 1

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

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

Step 2

Raise $10$ to the power of $3$ .

${(9 x \cdot \frac{1}{1000})}^{2}$

Step 3

Multiply $9 x \frac{1}{1000}$ .

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Step 3.1

Combine $9$ and $\frac{1}{1000}$ .

${(x \frac{9}{1000})}^{2}$

Step 3.2

Combine $x$ and $\frac{9}{1000}$ .

${(\frac{x \cdot 9}{1000})}^{2}$

Step 4

Move $9$ to the left of $x$ .

${(\frac{9 \cdot x}{1000})}^{2}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{9 x}{1000}$ .

$\frac{{(9 x)}^{2}}{1000^{2}}$

Step 5.2

Apply the product rule to $9 x$ .

$\frac{9^{2} x^{2}}{1000^{2}}$

Step 6

Raise $9$ to the power of $2$ .

$\frac{81 x^{2}}{1000^{2}}$

Step 7

Raise $1000$ to the power of $2$ .

$\frac{81 x^{2}}{1000000}$