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

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

Step 1

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

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

Step 2

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

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

Step 3

Move $x^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 4

Multiply $x^{\frac{6}{5}}$ by $x^{- 1}$ by adding the exponents.

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

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

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $6$ .

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

Step 5

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$a = 0.2$