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

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

Step 1

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

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

Step 2

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

Multiply $x^{\frac{6}{5}}$ by $x$ .

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

$x^{a} = x^{\frac{6}{5}} x^{1}$

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

$x^{a} = x^{\frac{6}{5} + 1}$

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

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

Combine the numerators over the common denominator.

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

Add $6$ and $5$ .

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

Step 3

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 2.2$

Mixed Number Form:

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