Simplify 1/((48x^3y^4)^-2)

$\frac{1}{{(48 x^{3} y^{4})}^{- 2}}$

Step 1

Move ${(48 x^{3} y^{4})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(48 x^{3} y^{4})}^{2}$

Step 2

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

Apply the product rule to $48 x^{3} y^{4}$ .

${(48 x^{3})}^{2} {(y^{4})}^{2}$

Apply the product rule to $48 x^{3}$ .

$48^{2} {(x^{3})}^{2} {(y^{4})}^{2}$

Step 3

Raise $48$ to the power of $2$ .

$2304 {(x^{3})}^{2} {(y^{4})}^{2}$

Step 4

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

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

$2304 x^{3 \cdot 2} {(y^{4})}^{2}$

Multiply $3$ by $2$ .

$2304 x^{6} {(y^{4})}^{2}$

Step 5

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

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

$2304 x^{6} y^{4 \cdot 2}$

Multiply $4$ by $2$ .

$2304 x^{6} y^{8}$