Algebra Examples

x^{2} \cdot x^{n} = {(x^{3})}^{4}

$x^{2} \cdot x^{n} = {(x^{3})}^{4}$

Step 1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

x^{2} \cdot x^{n} = x^{3 \cdot 4}

$x^{2} \cdot x^{n} = x^{3 \cdot 4}$

Step 2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

x^{2 + n} = x^{3 \cdot 4}

$x^{2 + n} = x^{3 \cdot 4}$

Step 3

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

2 + n = 3 \cdot 4

$2 + n = 3 \cdot 4$

Step 4

Solve for

n

$n$ .

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Step 4.1

Multiply

3

$3$ by

4

$4$ .

2 + n = 12

$2 + n = 12$

Step 4.2

Move all terms not containing

n

$n$ to the right side of the equation.

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Step 4.2.1

Subtract

2

$2$ from both sides of the equation.

n = 12 - 2

$n = 12 - 2$

Step 4.2.2

Subtract

2

$2$ from

12

$12$ .

n = 10

$n = 10$

n = 10

$n = 10$

n = 10

$n = 10$