Algebra Examples

$x^{\frac{1}{6}} x^{\frac{5}{6}} = x^{a}$

Step 1

Rewrite the equation as $x^{a} = x^{\frac{1}{6}} x^{\frac{5}{6}}$ .

$x^{a} = x^{\frac{1}{6}} x^{\frac{5}{6}}$

Step 2

Multiply $x^{\frac{1}{6}}$ by $x^{\frac{5}{6}}$ by adding the exponents.

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Step 2.1

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

$x^{a} = x^{\frac{1}{6} + \frac{5}{6}}$

Step 2.2

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{1 + 5}{6}}$

Step 2.3

Add $1$ and $5$ .

$x^{a} = x^{\frac{6}{6}}$

Step 2.4

Divide $6$ by $6$ .

$x^{a} = x^{1}$

Step 3

Simplify $x^{1}$ .

$x^{a} = x$

Step 4

Create equivalent expressions in the equation that all have equal bases.

$x^{a} = x^{1}$

Step 5

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

$a = 1$