Algebra Examples

${(2 \frac{12}{5} x^{2})}^{\frac{5}{3}}$

Step 1

Convert $2 \frac{12}{5}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

${((2 + \frac{12}{5}) x^{2})}^{\frac{5}{3}}$

Step 1.2

Add $2$ and $\frac{12}{5}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

${((2 \cdot \frac{5}{5} + \frac{12}{5}) x^{2})}^{\frac{5}{3}}$

Step 1.2.2

Combine $2$ and $\frac{5}{5}$ .

${((\frac{2 \cdot 5}{5} + \frac{12}{5}) x^{2})}^{\frac{5}{3}}$

Step 1.2.3

Combine the numerators over the common denominator.

${(\frac{2 \cdot 5 + 12}{5} x^{2})}^{\frac{5}{3}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

${(\frac{10 + 12}{5} x^{2})}^{\frac{5}{3}}$

Step 1.2.4.2

Add $10$ and $12$ .

${(\frac{22}{5} x^{2})}^{\frac{5}{3}}$

Step 2

Combine $\frac{22}{5}$ and $x^{2}$ .

${(\frac{22 x^{2}}{5})}^{\frac{5}{3}}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $\frac{22 x^{2}}{5}$ .

$\frac{{(22 x^{2})}^{\frac{5}{3}}}{5^{\frac{5}{3}}}$

Step 3.2

Apply the product rule to $22 x^{2}$ .

$\frac{22^{\frac{5}{3}} {(x^{2})}^{\frac{5}{3}}}{5^{\frac{5}{3}}}$

Step 4

Multiply the exponents in ${(x^{2})}^{\frac{5}{3}}$ .

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Step 4.1

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

$\frac{22^{\frac{5}{3}} x^{2 (\frac{5}{3})}}{5^{\frac{5}{3}}}$

Step 4.2

Multiply $2 (\frac{5}{3})$ .

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Step 4.2.1

Combine $2$ and $\frac{5}{3}$ .

$\frac{22^{\frac{5}{3}} x^{\frac{2 \cdot 5}{3}}}{5^{\frac{5}{3}}}$

Step 4.2.2

Multiply $2$ by $5$ .

$\frac{22^{\frac{5}{3}} x^{\frac{10}{3}}}{5^{\frac{5}{3}}}$