Basic Math Examples

${(\frac{27}{8})}^{\frac{2}{3}} - \frac{1}{8}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{27}{8}$ .

$\frac{27^{\frac{2}{3}}}{8^{\frac{2}{3}}} - \frac{1}{8}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Rewrite $27$ as $3^{3}$ .

$\frac{{(3^{3})}^{\frac{2}{3}}}{8^{\frac{2}{3}}} - \frac{1}{8}$

Step 1.2.2

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

$\frac{3^{3 (\frac{2}{3})}}{8^{\frac{2}{3}}} - \frac{1}{8}$

Step 1.2.3

Cancel the common factor of $3$ .

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Step 1.2.3.1

Cancel the common factor.

$\frac{3^{3 (\frac{2}{3})}}{8^{\frac{2}{3}}} - \frac{1}{8}$

Step 1.2.3.2

Rewrite the expression.

$\frac{3^{2}}{8^{\frac{2}{3}}} - \frac{1}{8}$

Step 1.2.4

Raise $3$ to the power of $2$ .

$\frac{9}{8^{\frac{2}{3}}} - \frac{1}{8}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

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

$\frac{9}{{(2^{3})}^{\frac{2}{3}}} - \frac{1}{8}$

Step 1.3.2

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

$\frac{9}{2^{3 (\frac{2}{3})}} - \frac{1}{8}$

Step 1.3.3

Cancel the common factor of $3$ .

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Step 1.3.3.1

Cancel the common factor.

$\frac{9}{2^{3 (\frac{2}{3})}} - \frac{1}{8}$

Step 1.3.3.2

Rewrite the expression.

$\frac{9}{2^{2}} - \frac{1}{8}$

Step 1.3.4

Raise $2$ to the power of $2$ .

$\frac{9}{4} - \frac{1}{8}$

Step 2

To write $\frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{4} \cdot \frac{2}{2} - \frac{1}{8}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{4 \cdot 2} - \frac{1}{8}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{9 \cdot 2}{8} - \frac{1}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 2 - 1}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $9$ by $2$ .

$\frac{18 - 1}{8}$

Step 5.2

Subtract $1$ from $18$ .

$\frac{17}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{8}$

Decimal Form:

$2.125$

Mixed Number Form:

$2 \frac{1}{8}$