Question

1. simplify: $-4x^{5}(3x^{-2}y^{0})$

a. $-12/x^{3}$
b. $-12x^{3}$
c. $-12x^{7}$
d. $-7x^{3}$

Explanation:

Step1: Recall the zero exponent rule

Any non - zero number to the power of 0 is 1, so \(y^{0}=1\) (assuming \(y
eq0\)). The expression becomes \(- 4x^{5}(3x^{-2}\times1)=-4x^{5}(3x^{-2})\)

Step2: Multiply the coefficients and use the product rule for exponents

The product rule for exponents is \(a^{m}\times a^{n}=a^{m + n}\). First, multiply the coefficients: \(-4\times3=-12\). Then, for the \(x\) terms, \(x^{5}\times x^{-2}=x^{5+( - 2)}=x^{3}\)

Step3: Combine the results

Combining the coefficient and the \(x\) term, we get \(-12x^{3}\)

Answer:

B. \(-12x^{3}\)