Solve for b (b^2)^0=b^8

${(b^{2})}^{0} = b^{8}$

Step 1

Simplify ${(b^{2})}^{0}$ .

Multiply the exponents in ${(b^{2})}^{0}$ .

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

$b^{2 \cdot 0} = b^{8}$

Multiply $2$ by $0$ .

$b^{0} = b^{8}$

Anything raised to $0$ is $1$ .

$1 = b^{8}$

Step 2

Since $b$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$b^{8} = 1$

Step 3

Take the 8th root of both sides of the equation to eliminate the exponent on the left side.

$b = \pm \sqrt[8]{1}$

Step 4

Any root of $1$ is $1$ .

$b = \pm 1$

Step 5

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

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

$b = 1$

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

$b = - 1$

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

$b = 1, - 1$