Simplify (8x^0y^2z^3)^-2

${(8 x^{0} y^{2} z^{3})}^{- 2}$

Step 1

Anything raised to $0$ is $1$ .

${(8 \cdot 1 y^{2} z^{3})}^{- 2}$

Step 2

Multiply $8$ by $1$ .

${(8 y^{2} z^{3})}^{- 2}$

Step 3

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

$\frac{1}{{(8 y^{2} z^{3})}^{2}}$

Step 4

Simplify the denominator.

Apply the product rule to $8 y^{2} z^{3}$ .

$\frac{1}{{(8 y^{2})}^{2} {(z^{3})}^{2}}$

Apply the product rule to $8 y^{2}$ .

$\frac{1}{8^{2} {(y^{2})}^{2} {(z^{3})}^{2}}$

Raise $8$ to the power of $2$ .

$\frac{1}{64 {(y^{2})}^{2} {(z^{3})}^{2}}$

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

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

$\frac{1}{64 y^{2 \cdot 2} {(z^{3})}^{2}}$

Multiply $2$ by $2$ .

$\frac{1}{64 y^{4} {(z^{3})}^{2}}$

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

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

$\frac{1}{64 y^{4} z^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{1}{64 y^{4} z^{6}}$