Simplify (2a^-3b^4c^0)^2

${(2 a^{- 3} b^{4} c^{0})}^{2}$

Step 1

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

${(2 \frac{1}{a^{3}} b^{4} c^{0})}^{2}$

Step 2

Combine $2$ and $\frac{1}{a^{3}}$ .

${(\frac{2}{a^{3}} b^{4} c^{0})}^{2}$

Step 3

Combine $\frac{2}{a^{3}}$ and $b^{4}$ .

${(\frac{2 b^{4}}{a^{3}} c^{0})}^{2}$

Step 4

Simplify the expression.

Anything raised to $0$ is $1$ .

${(\frac{2 b^{4}}{a^{3}} \cdot 1)}^{2}$

Multiply $\frac{2 b^{4}}{a^{3}}$ by $1$ .

${(\frac{2 b^{4}}{a^{3}})}^{2}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 b^{4}}{a^{3}}$ .

$\frac{{(2 b^{4})}^{2}}{{(a^{3})}^{2}}$

Apply the product rule to $2 b^{4}$ .

$\frac{2^{2} {(b^{4})}^{2}}{{(a^{3})}^{2}}$

Step 6

Simplify the numerator.

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

$\frac{4 {(b^{4})}^{2}}{{(a^{3})}^{2}}$

Multiply the exponents in ${(b^{4})}^{2}$ .

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

$\frac{4 b^{4 \cdot 2}}{{(a^{3})}^{2}}$

Multiply $4$ by $2$ .

$\frac{4 b^{8}}{{(a^{3})}^{2}}$

Step 7

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

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

$\frac{4 b^{8}}{a^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{4 b^{8}}{a^{6}}$