Algebra Examples

${(7^{2})}^{4} = n^{8}$

Step 1

Rewrite the equation as $n^{8} = {(7^{2})}^{4}$ .

$n^{8} = {(7^{2})}^{4}$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$n = \pm \sqrt[8]{{(7^{2})}^{4}}$

Step 3

Simplify $\pm \sqrt[8]{{(7^{2})}^{4}}$ .

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Step 3.1

Multiply the exponents in ${(7^{2})}^{4}$ .

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Step 3.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$n = \pm \sqrt[8]{7^{2 \cdot 4}}$

Step 3.1.2

Multiply $2$ by $4$ .

$n = \pm \sqrt[8]{7^{8}}$

Step 3.2

Raise $7$ to the power of $8$ .

$n = \pm \sqrt[8]{5764801}$

Step 3.3

Rewrite $5764801$ as $7^{8}$ .

$n = \pm \sqrt[8]{7^{8}}$

Step 3.4

Pull terms out from under the radical, assuming positive real numbers.

$n = \pm 7$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$n = 7$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$n = - 7$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$n = 7, - 7$