Solve for a xx^(3/4)=x^a

$x \cdot x^{\frac{3}{4}} = x^{a}$

Step 1

Rewrite the equation as $x^{a} = x \cdot x^{\frac{3}{4}}$ .

$x^{a} = x \cdot x^{\frac{3}{4}}$

Step 2

Multiply $x$ by $x^{\frac{3}{4}}$ by adding the exponents.

Multiply $x$ by $x^{\frac{3}{4}}$ .

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

$x^{a} = x^{1} x^{\frac{3}{4}}$

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

$x^{a} = x^{1 + \frac{3}{4}}$

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

$x^{a} = x^{\frac{4}{4} + \frac{3}{4}}$

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{4 + 3}{4}}$

Add $4$ and $3$ .

$x^{a} = x^{\frac{7}{4}}$

Step 3

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

$a = \frac{7}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{7}{4}$

Decimal Form:

$a = 1.75$

Mixed Number Form:

$a = 1 \frac{3}{4}$