Pre-Algebra Examples

$4.5 x \cdot 10^{9} x^{8} \cdot \frac{1}{2}$

Step 1

Write $4.5 x \cdot 10^{9} x^{8} \cdot \frac{1}{2}$ as an equation.

$y = 4.5 x \cdot 10^{9} x^{8} \cdot \frac{1}{2}$

Step 2

Simplify $4.5 x \cdot 10^{9} x^{8} \cdot \frac{1}{2}$ .

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Step 2.1

Multiply $x$ by $x^{8}$ by adding the exponents.

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Step 2.1.1

Move $x^{8}$ .

$y = 4.5 (x^{8} x) \cdot 10^{9} \cdot \frac{1}{2}$

Step 2.1.2

Multiply $x^{8}$ by $x$ .

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Step 2.1.2.1

Raise $x$ to the power of $1$ .

$y = 4.5 (x^{8} x^{1}) \cdot 10^{9} \cdot \frac{1}{2}$

Step 2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 4.5 x^{8 + 1} \cdot 10^{9} \cdot \frac{1}{2}$

Step 2.1.3

Add $8$ and $1$ .

$y = 4.5 x^{9} \cdot 10^{9} \cdot \frac{1}{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Raise $10$ to the power of $9$ .

$y = 4.5 x^{9} \cdot 1000000000 \cdot \frac{1}{2}$

Step 2.2.2

Multiply $1000000000$ by $4.5$ .

$y = 4500000000 x^{9} \cdot \frac{1}{2}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $4500000000 x^{9}$ .

$y = 2 (2250000000 x^{9}) \cdot \frac{1}{2}$

Step 2.3.2

Cancel the common factor.

$y = 2 (2250000000 x^{9}) \cdot \frac{1}{2}$

Step 2.3.3

Rewrite the expression.

$y = 2250000000 x^{9}$

Step 3

The given equation $y = 2250000000 x^{9}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$