Solve for a x^2x^(1/5)=x^a

$x^{2} x^{\frac{1}{5}} = x^{a}$

Rewrite the equation as $x^{a} = x^{2} x^{\frac{1}{5}}$ .

$x^{a} = x^{2} x^{\frac{1}{5}}$

Multiply $x^{2}$ by $x^{\frac{1}{5}}$ by adding the exponents.

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

$x^{a} = x^{2 + \frac{1}{5}}$

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

$x^{a} = x^{2 \cdot \frac{5}{5} + \frac{1}{5}}$

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

$x^{a} = x^{\frac{2 \cdot 5}{5} + \frac{1}{5}}$

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{2 \cdot 5 + 1}{5}}$

Simplify the numerator.

Multiply $2$ by $5$ .

$x^{a} = x^{\frac{10 + 1}{5}}$

Add $10$ and $1$ .

$x^{a} = x^{\frac{11}{5}}$

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

$a = \frac{11}{5}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{11}{5}$

Decimal Form:

$a = 2.2$

Mixed Number Form:

$a = 2 \frac{1}{5}$