Algebra Examples

$13 (8^{\frac{3}{4}}) - 4 \cdot 8^{\frac{3}{4}}$

Step 1

Factor out negative.

$13 \cdot 8^{\frac{3}{4}} - (4 \cdot 8^{\frac{3}{4}})$

Step 2

Rewrite $4$ as $2^{2}$ .

$13 \cdot 8^{\frac{3}{4}} - (2^{2} \cdot 8^{\frac{3}{4}})$

Step 3

Rewrite $8$ as $2^{3}$ .

$13 \cdot 8^{\frac{3}{4}} - (2^{2} \cdot {(2^{3})}^{\frac{3}{4}})$

Step 4

Multiply the exponents in ${(2^{3})}^{\frac{3}{4}}$ .

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Step 4.1

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

$13 \cdot 8^{\frac{3}{4}} - (2^{2} \cdot 2^{3 (\frac{3}{4})})$

Step 4.2

Multiply $3 (\frac{3}{4})$ .

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Step 4.2.1

Combine $3$ and $\frac{3}{4}$ .

$13 \cdot 8^{\frac{3}{4}} - (2^{2} \cdot 2^{\frac{3 \cdot 3}{4}})$

Step 4.2.2

Multiply $3$ by $3$ .

$13 \cdot 8^{\frac{3}{4}} - (2^{2} \cdot 2^{\frac{9}{4}})$

Step 5

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

$13 \cdot 8^{\frac{3}{4}} - 2^{2 + \frac{9}{4}}$

Step 6

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$13 \cdot 8^{\frac{3}{4}} - 2^{2 \cdot \frac{4}{4} + \frac{9}{4}}$

Step 7

Combine $2$ and $\frac{4}{4}$ .

$13 \cdot 8^{\frac{3}{4}} - 2^{\frac{2 \cdot 4}{4} + \frac{9}{4}}$

Step 8

Combine the numerators over the common denominator.

$13 \cdot 8^{\frac{3}{4}} - 2^{\frac{2 \cdot 4 + 9}{4}}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $2$ by $4$ .

$13 \cdot 8^{\frac{3}{4}} - 2^{\frac{8 + 9}{4}}$

Step 9.2

Add $8$ and $9$ .

$13 \cdot 8^{\frac{3}{4}} - 2^{\frac{17}{4}}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$13 \cdot 8^{\frac{3}{4}} - 2^{\frac{17}{4}}$

Decimal Form:

$42.81145614 \dots$