Question

1. fully simplify. $x^{2}y^{5}(-7x^{5}y^{2})$
2. fully simplify. $-6x^{5}y^{5}(11x^{5})$

Explanation:

Step1: Multiply coefficients and group like terms

$x^2y^5(-7x^5y^2) = -7 \cdot (x^2 \cdot x^5) \cdot (y^5 \cdot y^2)$

Step2: Apply exponent rule $a^m \cdot a^n=a^{m+n}$

$-7 \cdot x^{2+5} \cdot y^{5+2} = -7x^7y^7$

Step3: Multiply coefficients and group like terms

$-6x^5y^5(11x^5) = (-6 \cdot 11) \cdot (x^5 \cdot x^5) \cdot y^5$

Step4: Apply exponent rule $a^m \cdot a^n=a^{m+n}$

$-66 \cdot x^{5+5} \cdot y^5 = -66x^{10}y^5$

Answer:

1. $-7x^7y^7$
2. $-66x^{10}y^5$