Algebra Examples

$\frac{x^{5} \cdot x^{3}}{x^{4}} = \frac{x^{8}}{x^{4}}$

Step 1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x^{5} \cdot x^{3} = x^{8}$

Step 2

Multiply $x^{5}$ by $x^{3}$ 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.

$x^{5 + 3} = x^{8}$

Step 2.2

Add $5$ and $3$ .

$x^{8} = x^{8}$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $x^{8}$ from both sides of the equation.

$x^{8} - x^{8} = 0$

Step 3.2

Subtract $x^{8}$ from $x^{8}$ .

$0 = 0$

Step 4

Since $0 = 0$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$