Simplify (4z^3)^2(2z^0)^-2

${(4 z^{3})}^{2} {(2 z^{0})}^{- 2}$

Step 1

Apply the product rule to $4 z^{3}$ .

$4^{2} {(z^{3})}^{2} {(2 z^{0})}^{- 2}$

Step 2

Raise $4$ to the power of $2$ .

$16 {(z^{3})}^{2} {(2 z^{0})}^{- 2}$

Step 3

Multiply the exponents in ${(z^{3})}^{2}$ .

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

$16 z^{3 \cdot 2} {(2 z^{0})}^{- 2}$

Multiply $3$ by $2$ .

$16 z^{6} {(2 z^{0})}^{- 2}$

Step 4

Anything raised to $0$ is $1$ .

$16 z^{6} {(2 \cdot 1)}^{- 2}$

Step 5

Multiply $2$ by $1$ .

$16 z^{6} \cdot 2^{- 2}$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$16 z^{6} \cdot \frac{1}{2^{2}}$

Step 7

Raise $2$ to the power of $2$ .

$16 z^{6} \cdot \frac{1}{4}$

Step 8

Cancel the common factor of $4$ .

Factor $4$ out of $16 z^{6}$ .

$4 (4 z^{6}) \cdot \frac{1}{4}$

Cancel the common factor.

$4 (4 z^{6}) \cdot \frac{1}{4}$

Rewrite the expression.

$4 z^{6}$