Algebra Examples

16^{x^{2}} = 8^{0}

$16^{x^{2}} = 8^{0}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

2^{4 x^{2}} = 2^{3 \cdot 0}

$2^{4 x^{2}} = 2^{3 \cdot 0}$

Step 2

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

4 x^{2} = 3 \cdot 0

$4 x^{2} = 3 \cdot 0$

Step 3

Solve for

x

$x$ .

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Step 3.1

Multiply

3

$3$ by

0

$0$ .

4 x^{2} = 0

$4 x^{2} = 0$

Step 3.2

Divide each term in

4 x^{2} = 0

$4 x^{2} = 0$ by

4

$4$ and simplify.

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Step 3.2.1

Divide each term in

4 x^{2} = 0

$4 x^{2} = 0$ by

4

$4$ .

\frac{4 x^{2}}{4} = \frac{0}{4}

$\frac{4 x^{2}}{4} = \frac{0}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

4

$4$ .

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Step 3.2.2.1.1

Cancel the common factor.

\frac{4 x^{2}}{4} = \frac{0}{4}

$\frac{4 x^{2}}{4} = \frac{0}{4}$

Step 3.2.2.1.2

Divide

x^{2}

$x^{2}$ by

1

$1$ .

x^{2} = \frac{0}{4}

$x^{2} = \frac{0}{4}$

x^{2} = \frac{0}{4}

$x^{2} = \frac{0}{4}$

x^{2} = \frac{0}{4}

$x^{2} = \frac{0}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide

0

$0$ by

4

$4$ .

x^{2} = 0

$x^{2} = 0$

x^{2} = 0

$x^{2} = 0$

x^{2} = 0

$x^{2} = 0$

Step 3.3

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

x = \pm \sqrt{0}

$x = \pm \sqrt{0}$

Step 3.4

Simplify

\pm \sqrt{0}

$\pm \sqrt{0}$ .

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Step 3.4.1

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

x = \pm \sqrt{0^{2}}

$x = \pm \sqrt{0^{2}}$

Step 3.4.2

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

x = \pm 0

$x = \pm 0$

Step 3.4.3

Plus or minus

0

$0$ is

0

$0$ .

x = 0

$x = 0$

x = 0

$x = 0$

x = 0

$x = 0$

16^{x^{2}} = 8^{0}

$16^{x^{2}} = 8^{0}$

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