Solve for x 16^(x^2)=8^0

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

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

Multiply $3$ by $0$ .

$4 x^{2} = 0$

Divide each term in $4 x^{2} = 0$ by $4$ and simplify.

Divide each term in $4 x^{2} = 0$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x^{2}$ by $1$ .

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

Simplify the right side.

Divide $0$ by $4$ .

$x^{2} = 0$

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

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

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

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$