Algebra Examples

$x^{\frac{5}{3}} x^{2} = x^{a}$

Step 1

Rewrite the equation as $x^{a} = x^{\frac{5}{3}} x^{2}$ .

$x^{a} = x^{\frac{5}{3}} x^{2}$

Step 2

Multiply $x^{\frac{5}{3}}$ by $x^{2}$ by adding the exponents.

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Step 2.1

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

$x^{a} = x^{\frac{5}{3} + 2}$

Step 2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{a} = x^{\frac{5}{3} + 2 \cdot \frac{3}{3}}$

Step 2.3

Combine $2$ and $\frac{3}{3}$ .

$x^{a} = x^{\frac{5}{3} + \frac{2 \cdot 3}{3}}$

Step 2.4

Combine the numerators over the common denominator.

$x^{a} = x^{\frac{5 + 2 \cdot 3}{3}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $3$ .

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

Step 2.5.2

Add $5$ and $6$ .

$x^{a} = x^{\frac{11}{3}}$

Step 3

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

$a = \frac{11}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{11}{3}$

Decimal Form:

$a = 3.\overline{6}$

Mixed Number Form:

$a = 3 \frac{2}{3}$