Simplify 3x^-2y^4*4x^-2

$3 x^{- 2} y^{4} \cdot 4 x^{- 2}$

Step 1

Multiply $x^{- 2}$ by $x^{- 2}$ by adding the exponents.

Move $x^{- 2}$ .

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

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

$3 x^{- 2 - 2} y^{4} \cdot 4$

Subtract $2$ from $- 2$ .

$3 x^{- 4} y^{4} \cdot 4$

Step 2

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

$3 \frac{1}{x^{4}} y^{4} \cdot 4$

Step 3

Combine $3$ and $\frac{1}{x^{4}}$ .

$\frac{3}{x^{4}} y^{4} \cdot 4$

Step 4

Combine $\frac{3}{x^{4}}$ and $y^{4}$ .

$\frac{3 y^{4}}{x^{4}} \cdot 4$

Step 5

Multiply $\frac{3 y^{4}}{x^{4}} \cdot 4$ .

Combine $\frac{3 y^{4}}{x^{4}}$ and $4$ .

$\frac{3 y^{4} \cdot 4}{x^{4}}$

Multiply $4$ by $3$ .

$\frac{12 y^{4}}{x^{4}}$