Algebra Examples

$2 d^{12} \cdot \frac{d^{- 2}}{d^{6}}$

Step 1

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

$2 d^{12} \cdot \frac{\frac{1}{d^{2}}}{d^{6}}$

Step 2

Cancel the common factor of $d^{6}$ .

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Step 2.1

Factor $d^{6}$ out of $2 d^{12}$ .

$d^{6} (2 d^{6}) \cdot \frac{\frac{1}{d^{2}}}{d^{6}}$

Step 2.2

Cancel the common factor.

$d^{6} (2 d^{6}) \cdot \frac{\frac{1}{d^{2}}}{d^{6}}$

Step 2.3

Rewrite the expression.

$2 d^{6} \cdot \frac{1}{d^{2}}$

Step 3

Combine $2$ and $\frac{1}{d^{2}}$ .

$d^{6} \cdot \frac{2}{d^{2}}$

Step 4

Combine $d^{6}$ and $\frac{2}{d^{2}}$ .

$\frac{d^{6} \cdot 2}{d^{2}}$

Step 5

Cancel the common factor of $d^{6}$ and $d^{2}$ .

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Step 5.1

Factor $d^{2}$ out of $d^{6} \cdot 2$ .

$\frac{d^{2} (d^{4} \cdot 2)}{d^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\frac{d^{2} (d^{4} \cdot 2)}{d^{2} \cdot 1}$

Step 5.2.2

Cancel the common factor.

$\frac{d^{2} (d^{4} \cdot 2)}{d^{2} \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{d^{4} \cdot 2}{1}$

Step 5.2.4

Divide $d^{4} \cdot 2$ by $1$ .

$d^{4} \cdot 2$

Step 6

Move $2$ to the left of $d^{4}$ .

$2 d^{4}$