Question

1. simplify each expression. show all work. a. (2m³)(4m²) b. (6y⁵)/(3y²) c. (-4y²)/(6y⁷) d. (-2x²)³

Explanation:

Step1: Multiply coefficients, add exponents

$(2m^3)(4m^2) = (2 \times 4)m^{3+2}$

Step2: Simplify the result

$= 8m^5$

Step1: Divide coefficients, subtract exponents

$\frac{6y^5}{3y^2} = \frac{6}{3}y^{5-2}$

Step2: Simplify the result

$= 2y^3$

Step1: Reduce fraction, subtract exponents

$\frac{-4y^2}{6y^7} = \frac{-4}{6}y^{2-7}$

Step2: Simplify the result

$= -\frac{2}{3}y^{-5} = \frac{-2}{3y^5}$

Step1: Distribute exponent to each term

$(-2x^2)^3 = (-2)^3 \times (x^2)^3$

Step2: Calculate powers, multiply exponents

$= -8x^{2 \times 3} = -8x^6$

Answer:

a. $8m^5$
b. $2y^3$
c. $\frac{-2}{3y^5}$
d. $-8x^6$