Pre-Algebra Examples

$\frac{{(1.2 x \cdot 10^{- 3})}^{2}}{{(10^{- 2})}^{3} \cdot (2 x \cdot 10^{- 3})}$

Step 1

Move $10^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(1.2 x \cdot 10^{- 3})}^{2} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot (2 x)}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $1.2 x \cdot 10^{- 3}$ .

$\frac{{(1.2 x)}^{2} \cdot {(10^{- 3})}^{2} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.2

Apply the product rule to $1.2 x$ .

$\frac{{1.2}^{2} x^{2} \cdot {(10^{- 3})}^{2} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.3

Raise $1.2$ to the power of $2$ .

$\frac{1.44 x^{2} \cdot {(10^{- 3})}^{2} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.4

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

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Step 2.4.1

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

$\frac{1.44 x^{2} \cdot 10^{- 3 \cdot 2} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.4.2

Multiply $- 3$ by $2$ .

$\frac{1.44 x^{2} \cdot 10^{- 6} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.5

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

$\frac{1.44 x^{2} \cdot \frac{1}{10^{6}} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.6

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

$\frac{1.44 x^{2} \cdot \frac{1}{1000000} \cdot 10^{3}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.7

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

$\frac{1.44 x^{2} \cdot \frac{1}{1000000} \cdot 1000}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.8

Combine exponents.

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Step 2.8.1

Combine $1.44$ and $\frac{1}{1000000}$ .

$\frac{x^{2} \cdot \frac{1.44}{1000000} \cdot 1000}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.8.2

Combine $x^{2}$ and $\frac{1.44}{1000000}$ .

$\frac{\frac{x^{2} \cdot 1.44}{1000000} \cdot 1000}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.8.3

Combine $\frac{x^{2} \cdot 1.44}{1000000}$ and $1000$ .

$\frac{\frac{x^{2} \cdot 1.44 \cdot 1000}{1000000}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.8.4

Multiply $1000$ by $1.44$ .

$\frac{\frac{x^{2} \cdot 1440}{1000000}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.9

Reduce the expression $\frac{x^{2} \cdot 1440}{1000000}$ by cancelling the common factors.

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Step 2.9.1

Factor $160$ out of $x^{2} \cdot 1440$ .

$\frac{\frac{160 (x^{2} \cdot 9)}{1000000}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.9.2

Factor $160$ out of $1000000$ .

$\frac{\frac{160 (x^{2} \cdot 9)}{160 (6250)}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.9.3

Cancel the common factor.

$\frac{\frac{160 (x^{2} \cdot 9)}{160 \cdot 6250}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.9.4

Rewrite the expression.

$\frac{\frac{x^{2} \cdot 9}{6250}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 2.10

Move $9$ to the left of $x^{2}$ .

$\frac{\frac{9 x^{2}}{6250}}{{(10^{- 2})}^{3} \cdot 2 x}$

Step 3

Multiply ${(10^{- 2})}^{3}$ by $2$ .

$\frac{\frac{9 x^{2}}{6250}}{0.000002 x}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{9 x^{2}}{6250} \cdot \frac{1}{0.000002 x}$

Step 5

Combine.

$\frac{9 x^{2} \cdot 1}{6250 (0.000002 x)}$

Step 6

Cancel the common factor of $x^{2}$ and $x$ .

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Step 6.1

Factor $x$ out of $9 x^{2} \cdot 1$ .

$\frac{x (9 x \cdot 1)}{6250 (0.000002 x)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $x$ out of $6250 (0.000002 x)$ .

$\frac{x (9 x \cdot 1)}{x (6250 \cdot (0.000002))}$

Step 6.2.2

Cancel the common factor.

$\frac{x (9 x \cdot 1)}{x (6250 \cdot (0.000002))}$

Step 6.2.3

Rewrite the expression.

$\frac{9 x \cdot 1}{6250 \cdot (0.000002)}$

Step 7

Multiply $9$ by $1$ .

$\frac{9 x}{6250 \cdot (0.000002)}$

Step 8

Multiply $6250$ by $0.000002$ .

$\frac{9 x}{0.0125}$

Step 9

Factor $9$ out of $9 x$ .

$\frac{9 (x)}{0.0125}$

Step 10

Factor $0.0125$ out of $0.0125$ .

$\frac{9 (x)}{0.0125 (1)}$

Step 11

Separate fractions.

$\frac{9}{0.0125} \cdot \frac{x}{1}$

Step 12

Divide $9$ by $0.0125$ .

$720 \frac{x}{1}$

Step 13

Divide $x$ by $1$ .

$720 x$