Algebra Examples

$x^{\frac{1}{4}} \sqrt[4]{x^{3}} = x^{a}$

Step 1

Rewrite the equation as $x^{a} = x^{\frac{1}{4}} \sqrt[4]{x^{3}}$ .

$x^{a} = x^{\frac{1}{4}} \sqrt[4]{x^{3}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{3}}$ as $x^{\frac{3}{4}}$ .

$x^{a} = x^{\frac{1}{4}} x^{\frac{3}{4}}$

Step 3

Multiply $x^{\frac{1}{4}}$ by $x^{\frac{3}{4}}$ by adding the exponents.

Tap for more steps...

Step 3.1

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

$x^{a} = x^{\frac{1}{4} + \frac{3}{4}}$

Step 3.2

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{1 + 3}{4}}$

Step 3.3

Add $1$ and $3$ .

$x^{a} = x^{\frac{4}{4}}$

Step 3.4

Divide $4$ by $4$ .

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

Step 4

Simplify $x^{1}$ .

$x^{a} = x$

Step 5

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

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

Step 6

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

$a = 1$