Question

problem 15: (first taught in lesson 73)
multiply these fractions and select the simplified answer.
\\(\frac{8x^6}{9x^2} \cdot \frac{3x^3}{12x}\\)
after you pick your answer press go.
a. \\(\frac{2x^6}{9}\\) b. \\(\frac{2x^6}{3}\\) c. \\(\frac{8x^6 + 3x^3}{9x^2 + 12x}\\)
d. \\(\frac{11x^6}{21}\\) e. \\(\frac{32x^2}{9}\\)

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators \(8x^6\) and \(3x^3\), and the denominators \(9x^2\) and \(12x\). So we get \(\frac{8x^6 \cdot 3x^3}{9x^2 \cdot 12x}\). Using the rule of exponents \(a^m \cdot a^n=a^{m + n}\) and multiplying the coefficients, we have \(\frac{24x^{6+3}}{108x^{2 + 1}}=\frac{24x^9}{108x^3}\).

Step2: Simplify the fraction

Simplify the coefficient \(\frac{24}{108}=\frac{2}{9}\) (dividing numerator and denominator by 12). For the variable part, using the rule \(\frac{a^m}{a^n}=a^{m - n}\), we have \(x^{9-3}=x^6\). Combining these, we get \(\frac{2x^6}{9}\).

Answer:

A. \(\frac{2x^6}{9}\)