Solve for a xx^(4/5)=x^a

$x \cdot x^{\frac{4}{5}} = x^{a}$

Rewrite the equation as $x^{a} = x \cdot x^{\frac{4}{5}}$ .

$x^{a} = x \cdot x^{\frac{4}{5}}$

Multiply $x$ by $x^{\frac{4}{5}}$ by adding the exponents.

Multiply $x$ by $x^{\frac{4}{5}}$ .

Raise $x$ to the power of $1$ .

$x^{a} = x^{1} x^{\frac{4}{5}}$

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

$x^{a} = x^{1 + \frac{4}{5}}$

Write $1$ as a fraction with a common denominator.

$x^{a} = x^{\frac{5}{5} + \frac{4}{5}}$

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{5 + 4}{5}}$

Add $5$ and $4$ .

$x^{a} = x^{\frac{9}{5}}$

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

$a = \frac{9}{5}$

The result can be shown in multiple forms.

Exact Form:

$a = \frac{9}{5}$

Decimal Form:

$a = 1.8$

Mixed Number Form:

$a = 1 \frac{4}{5}$