Algebra Examples

$x \cdot x^{\frac{4}{5}} = x^{a}$

Step 1

Rewrite the equation as $x^{a} = x \cdot x^{\frac{4}{5}}$ .

$x^{a} = x \cdot x^{\frac{4}{5}}$

Step 2

Multiply $x$ by $x^{\frac{4}{5}}$ by adding the exponents.

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Step 2.1

Multiply $x$ by $x^{\frac{4}{5}}$ .

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Step 2.1.1

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

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

Step 2.1.2

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

$x^{a} = x^{1 + \frac{4}{5}}$

Step 2.2

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

$x^{a} = x^{\frac{5}{5} + \frac{4}{5}}$

Step 2.3

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{5 + 4}{5}}$

Step 2.4

Add $5$ and $4$ .

$x^{a} = x^{\frac{9}{5}}$

Step 3

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

$a = \frac{9}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{9}{5}$

Decimal Form:

$a = 1.8$

Mixed Number Form:

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