Solve for a (x^(1/5))^3=x^a

${(x^{\frac{1}{5}})}^{3} = x^{a}$

Step 1

Rewrite the equation as $x^{a} = {(x^{\frac{1}{5}})}^{3}$ .

$x^{a} = {(x^{\frac{1}{5}})}^{3}$

Step 2

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

$x^{a} = x^{\frac{1}{5} \cdot 3}$

Step 3

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

$a = \frac{1}{5} \cdot 3$

Step 4

Combine $\frac{1}{5}$ and $3$ .

$a = \frac{3}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{3}{5}$

Decimal Form:

$a = 0.6$