Simplify (z^8)^0z^(1/2)

${(z^{8})}^{0} z^{\frac{1}{2}}$

Step 1

Multiply the exponents in ${(z^{8})}^{0}$ .

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

$z^{8 \cdot 0} z^{\frac{1}{2}}$

Multiply $8$ by $0$ .

$z^{0} z^{\frac{1}{2}}$

Step 2

Multiply $z^{0}$ by $z^{\frac{1}{2}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z^{0 + \frac{1}{2}}$

Add $0$ and $\frac{1}{2}$ .

$z^{\frac{1}{2}}$