Question

1. simplify the expression. ((x^{4}y^{7})^{-3}) type a response

Explanation:

Step1: Apply power of a product rule

$(ab)^n=a^n b^n$
So, $(x^4 y^7)^{-3}=(x^4)^{-3}(y^7)^{-3}$

Step2: Apply power of a power rule

$(a^m)^n=a^{m \cdot n}$
$(x^4)^{-3}=x^{4 \times (-3)}=x^{-12}$
$(y^7)^{-3}=y^{7 \times (-3)}=y^{-21}$

Step3: Rewrite with positive exponents

$a^{-n}=\frac{1}{a^n}$
$x^{-12}=\frac{1}{x^{12}}$, $y^{-21}=\frac{1}{y^{21}}$
Multiply the terms: $\frac{1}{x^{12}} \cdot \frac{1}{y^{21}}=\frac{1}{x^{12}y^{21}}$

Answer:

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