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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine $5$ and $\frac{1}{2}$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 2.5$

Mixed Number Form:

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