Solve for a x^3x^(6/5)=x^a

$x^{3} x^{\frac{6}{5}} = x^{a}$

Step 1

Rewrite the equation as $x^{a} = x^{3} x^{\frac{6}{5}}$ .

$x^{a} = x^{3} x^{\frac{6}{5}}$

Step 2

Multiply $x^{3}$ by $x^{\frac{6}{5}}$ by adding the exponents.

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

$x^{a} = x^{3 + \frac{6}{5}}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x^{a} = x^{3 \cdot \frac{5}{5} + \frac{6}{5}}$

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

$x^{a} = x^{\frac{3 \cdot 5}{5} + \frac{6}{5}}$

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{3 \cdot 5 + 6}{5}}$

Simplify the numerator.

Multiply $3$ by $5$ .

$x^{a} = x^{\frac{15 + 6}{5}}$

Add $15$ and $6$ .

$x^{a} = x^{\frac{21}{5}}$

Step 3

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

$a = \frac{21}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{21}{5}$

Decimal Form:

$a = 4.2$

Mixed Number Form:

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