Finite Math Examples

$\frac{{(\frac{w \cdot 7}{8})}^{3} w \cdot 1}{8}$

Step 1

Multiply ${(\frac{w \cdot 7}{8})}^{3}$ by $1$ .

$\frac{w \cdot {(\frac{w \cdot 7}{8})}^{3}}{8}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{w \cdot 7}{8}$ .

$\frac{w \frac{{(w \cdot 7)}^{3}}{8^{3}}}{8}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Apply the product rule to $w \cdot 7$ .

$\frac{w \frac{w^{3} \cdot 7^{3}}{8^{3}}}{8}$

Step 2.2.2

Raise $7$ to the power of $3$ .

$\frac{w \frac{w^{3} \cdot 343}{8^{3}}}{8}$

Step 2.3

Raise $8$ to the power of $3$ .

$\frac{w \frac{w^{3} \cdot 343}{512}}{8}$

Step 2.4

Move $343$ to the left of $w^{3}$ .

$\frac{w \frac{343 w^{3}}{512}}{8}$

Step 3

Combine $w$ and $\frac{343 w^{3}}{512}$ .

$\frac{\frac{w (343 w^{3})}{512}}{8}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{\frac{343 (w^{1} w^{3})}{512}}{8}$

Step 4.2

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

$\frac{\frac{343 w^{1 + 3}}{512}}{8}$

Step 4.3

Add $1$ and $3$ .

$\frac{\frac{343 w^{4}}{512}}{8}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{343 w^{4}}{512} \cdot \frac{1}{8}$

Step 6

Combine.

$\frac{343 w^{4} \cdot 1}{512 \cdot 8}$

Step 7

Multiply.

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Step 7.1

Multiply $343$ by $1$ .

$\frac{343 w^{4}}{512 \cdot 8}$

Step 7.2

Multiply $512$ by $8$ .

$\frac{343 w^{4}}{4096}$