Basic Math Examples

$\frac{a^{15}}{a^{5}} = a^{10}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{a^{15}}{a^{5}}$ by cancelling the common factors.

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Step 1.1.1

Factor $a^{5}$ out of $a^{15}$ .

$\frac{a^{5} a^{10}}{a^{5}} = a^{10}$

Step 1.1.2

Multiply by $1$ .

$\frac{a^{5} a^{10}}{a^{5} \cdot 1} = a^{10}$

Step 1.1.3

Cancel the common factor.

$\frac{a^{5} a^{10}}{a^{5} \cdot 1} = a^{10}$

Step 1.1.4

Rewrite the expression.

$\frac{a^{10}}{1} = a^{10}$

Step 1.2

Divide $a^{10}$ by $1$ .

$a^{10} = a^{10}$

Step 2

Solve the equation.

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Step 2.1

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| a | = | a |$

Step 2.2

Solve for $a$ .

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Step 2.2.1

Rewrite the absolute value equation as four equations without absolute value bars.

$a = a$

$a = - a$

$- a = a$

$- a = - a$

Step 2.2.2

After simplifying, there are only two unique equations to be solved.

$a = a$

$a = - a$

Step 2.2.3

Solve $a = a$ for $a$ .

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Step 2.2.3.1

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

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Step 2.2.3.1.1

Subtract $a$ from both sides of the equation.

$a - a = 0$

Step 2.2.3.1.2

Subtract $a$ from $a$ .

$0 = 0$

Step 2.2.3.2

Since $0 = 0$ , the equation will always be true.

All real numbers

Step 2.2.4

Solve $a = - a$ for $a$ .

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Step 2.2.4.1

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

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Step 2.2.4.1.1

Add $a$ to both sides of the equation.

$a + a = 0$

Step 2.2.4.1.2

Add $a$ and $a$ .

$2 a = 0$

Step 2.2.4.2

Divide each term in $2 a = 0$ by $2$ and simplify.

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Step 2.2.4.2.1

Divide each term in $2 a = 0$ by $2$ .

$\frac{2 a}{2} = \frac{0}{2}$

Step 2.2.4.2.2

Simplify the left side.

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Step 2.2.4.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.4.2.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{0}{2}$

Step 2.2.4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{0}{2}$

Step 2.2.4.2.3

Simplify the right side.

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Step 2.2.4.2.3.1

Divide $0$ by $2$ .

$a = 0$

Step 2.2.5

List all of the solutions.

$a = 0$

Step 3

Exclude the solutions that do not make $\frac{a^{15}}{a^{5}} = a^{10}$ true.

$No solution$