Question

1. simplify the expression.

$(x^{4}y^{7})^{-3}$

Explanation:

Step1: Apply power of a product rule

$(x^4 y^7)^{-3} = (x^4)^{-3} \cdot (y^7)^{-3}$

Step2: Apply power of a power rule

$(x^4)^{-3} = x^{4 \times (-3)} = x^{-12}$, $(y^7)^{-3} = y^{7 \times (-3)} = y^{-21}$

Step3: Rewrite with positive exponents

$x^{-12}y^{-21} = \frac{1}{x^{12}y^{21}}$

Answer:

$\frac{1}{x^{12}y^{21}}$