Basic Math Examples

$a^{100} = 2 + (n - 1) \cdot 4$

Step 1

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

$a = \pm \sqrt[100]{2 + (n - 1) \cdot 4}$

Step 2

Simplify $\pm \sqrt[100]{2 + (n - 1) \cdot 4}$ .

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Step 2.1

Factor $2$ out of $2 + (n - 1) \cdot 4$ .

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Step 2.1.1

Factor $2$ out of $2$ .

$a = \pm \sqrt[100]{2 (1) + (n - 1) \cdot 4}$

Step 2.1.2

Factor $2$ out of $(n - 1) \cdot 4$ .

$a = \pm \sqrt[100]{2 (1) + 2 ((n - 1) \cdot 2)}$

Step 2.1.3

Factor $2$ out of $2 (1) + 2 ((n - 1) \cdot 2)$ .

$a = \pm \sqrt[100]{2 (1 + (n - 1) \cdot 2)}$

Step 2.2

Apply the distributive property.

$a = \pm \sqrt[100]{2 (1 + n \cdot 2 - 1 \cdot 2)}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move $2$ to the left of $n$ .

$a = \pm \sqrt[100]{2 (1 + 2 \cdot n - 1 \cdot 2)}$

Step 2.3.2

Multiply $- 1$ by $2$ .

$a = \pm \sqrt[100]{2 (1 + 2 \cdot n - 2)}$

Step 2.3.3

Subtract $2$ from $1$ .

$a = \pm \sqrt[100]{2 (2 n - 1)}$

Step 3

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

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Step 3.1

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

$a = \sqrt[100]{2 (2 n - 1)}$

Step 3.2

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

$a = - \sqrt[100]{2 (2 n - 1)}$

Step 3.3

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

$a = \sqrt[100]{2 (2 n - 1)}, - \sqrt[100]{2 (2 n - 1)}$