Question

simplify. your answer should contain only positive exponents.

1. $-x^{4}y^{4}z^{4} \cdot 2x^{4}y^{2}z^{2}$
2. $\frac{3qp^{3}r^{2}}{3q^{4}r^{2}}$

Explanation:

Step1: Multiply coefficients and like bases

$(-1 \times 2) \cdot x^{4+4} \cdot y^{4+2} \cdot z^{4+2}$

Step2: Simplify exponents and coefficient

$-2x^{8}y^{6}z^{6}$

Step3: Cancel common coefficients and bases

$\frac{3}{3} \cdot q^{1-4} \cdot p^{3} \cdot r^{2-2}$

Step4: Simplify terms, convert negative exponents

$1 \cdot q^{-3} \cdot p^{3} \cdot 1 = \frac{p^{3}}{q^{3}}$

Answer:

1. $-2x^{8}y^{6}z^{6}$
2. $\frac{p^{3}}{q^{3}}$