Question

nt of powers property
simplify \\(\frac{15a^9be^4}{35a^5e^4}\\)
\\(\circ\\) \\(20a^3b\\)
\\(\circ\\) \\(\frac{3a^4b}{7}\\)
\\(\circ\\) \\(20a^4b\\)
\\(\circ\\) \\(\frac{3a^5b}{7}\\)
done

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients \( \frac{15}{35} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 5. So \( \frac{15\div5}{35\div5}=\frac{3}{7} \).

Step2: Simplify variable \(a\)

For the variable \(a\), we use the quotient of powers property \( \frac{a^m}{a^n}=a^{m - n} \). Here, \(m = 9\) and \(n = 5\), so \( \frac{a^9}{a^5}=a^{9 - 5}=a^4 \).

Step3: Simplify variable \(c\)

For the variable \(c\), using the quotient of powers property \( \frac{c^4}{c^4}=c^{4 - 4}=c^0 = 1\) (since any non - zero number to the power of 0 is 1, and we can assume \(c
eq0\) here). The variable \(b\) remains as it is since there is no \(b\) in the denominator.

Step4: Combine all parts

Combining the simplified coefficient, the simplified \(a\) term, the \(b\) term, and the simplified \(c\) term, we get \( \frac{3}{7}\times a^4\times b\times1=\frac{3a^4b}{7} \).

Answer:

\(\frac{3a^4b}{7}\) (corresponding to the option \(\frac{3a^4b}{7}\))