Question

simplify the expression. \\((-xy^{3}z)(x^{3}y^{4}z)(8x^{3}yz)\\)

Explanation:

Step1: Group like terms

$(-1 \times 8) \times (x \times x^2 \times x^3) \times (y^5 \times y^4) \times (z \times z \times z)$

Step2: Multiply coefficients

$-8 \times (x \times x^2 \times x^3) \times (y^5 \times y^4) \times (z \times z \times z)$

Step3: Combine x-terms (add exponents)

$-8 \times x^{1+2+3} \times (y^5 \times y^4) \times (z \times z \times z)$
$-8 \times x^6 \times (y^5 \times y^4) \times (z \times z \times z)$

Step4: Combine y-terms (add exponents)

$-8 \times x^6 \times y^{5+4} \times (z \times z \times z)$
$-8 \times x^6 \times y^9 \times (z \times z \times z)$

Step5: Combine z-terms (add exponents)

$-8 \times x^6 \times y^9 \times z^{1+1+1}$
$-8 \times x^6 \times y^9 \times z^3$

Answer:

$-8x^6y^9z^3$