Finite Math Examples

${(x^{\frac{5}{6}})}^{\frac{2}{15}} = x^{s}$

Step 1

Rewrite the equation as $x^{s} = {(x^{\frac{5}{6}})}^{\frac{2}{15}}$ .

$x^{s} = {(x^{\frac{5}{6}})}^{\frac{2}{15}}$

Step 2

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

$x^{s} = x^{\frac{5}{6} \cdot \frac{2}{15}}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$s = \frac{5}{6} \cdot \frac{2}{15}$

Step 4

Simplify $\frac{5}{6} \cdot \frac{2}{15}$ .

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Step 4.1

Cancel the common factor of $5$ .

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Step 4.1.1

Factor $5$ out of $15$ .

$s = \frac{5}{6} \cdot \frac{2}{5 (3)}$

Step 4.1.2

Cancel the common factor.

$s = \frac{5}{6} \cdot \frac{2}{5 \cdot 3}$

Step 4.1.3

Rewrite the expression.

$s = \frac{1}{6} \cdot \frac{2}{3}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $6$ .

$s = \frac{1}{2 (3)} \cdot \frac{2}{3}$

Step 4.2.2

Cancel the common factor.

$s = \frac{1}{2 \cdot 3} \cdot \frac{2}{3}$

Step 4.2.3

Rewrite the expression.

$s = \frac{1}{3} \cdot \frac{1}{3}$

Step 4.3

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

$s = \frac{1}{3 \cdot 3}$

Step 4.4

Multiply $3$ by $3$ .

$s = \frac{1}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$s = \frac{1}{9}$

Decimal Form:

$s = 0.\overline{1}$