Question

question
fully simplify using only positive exponents.
\frac{30x^{4}y^{6}}{20x^{3}y^{2}}
answer
attempt 1 out of 2
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Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients $\frac{30}{20}$. We can divide both the numerator and the denominator by their greatest common divisor, which is 10. So $\frac{30}{20}=\frac{30\div10}{20\div10}=\frac{3}{2}$.

Step2: Simplify the \(x\)-terms

For the \(x\)-terms, we use the quotient rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \). Here, \(a = x\), \(m = 4\), and \(n = 3\). So \(\frac{x^4}{x^3}=x^{4 - 3}=x\).

Step3: Simplify the \(y\)-terms

For the \(y\)-terms, we also use the quotient rule of exponents. Here, \(a = y\), \(m = 6\), and \(n = 2\). So \(\frac{y^6}{y^2}=y^{6 - 2}=y^4\).

Step4: Combine the simplified terms

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together. So we have \(\frac{3}{2}\times x\times y^4=\frac{3}{2}xy^4\).

Answer:

\(\frac{3}{2}xy^4\)