Algebra Examples

$\frac{d^{2}}{d} \cdot 8 d^{5}$

Step 1

Rewrite using the commutative property of multiplication.

$8 \frac{d^{2}}{d} d^{5}$

Step 2

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

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Step 2.1

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

$8 \frac{d \cdot d}{d} d^{5}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$8 \frac{d \cdot d}{d^{1}} d^{5}$

Step 2.2.2

Factor $d$ out of $d^{1}$ .

$8 \frac{d \cdot d}{d \cdot 1} d^{5}$

Step 2.2.3

Cancel the common factor.

$8 \frac{d \cdot d}{d \cdot 1} d^{5}$

Step 2.2.4

Rewrite the expression.

$8 \frac{d}{1} d^{5}$

Step 2.2.5

Divide $d$ by $1$ .

$8 d \cdot d^{5}$

Step 3

Multiply $d$ by $d^{5}$ by adding the exponents.

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Step 3.1

Move $d^{5}$ .

$8 (d^{5} d)$

Step 3.2

Multiply $d^{5}$ by $d$ .

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Step 3.2.1

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

$8 (d^{5} d^{1})$

Step 3.2.2

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

$8 d^{5 + 1}$

Step 3.3

Add $5$ and $1$ .

$8 d^{6}$