Question

question
fully simplify using only positive exponents.
\\(\frac{30x^8y^4}{12x^5y^6}\\)
answer attempt 1 out of 2

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \( \frac{30}{12} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 6. So, \( \frac{30\div6}{12\div6}=\frac{5}{2} \).

Step2: Simplify the \( x \)-terms

Using the quotient rule for exponents \( \frac{a^m}{a^n}=a^{m - n} \), for the \( x \)-terms \( \frac{x^8}{x^5} \), we have \( x^{8 - 5}=x^3 \).

Step3: Simplify the \( y \)-terms

Using the quotient rule for exponents again, for the \( y \)-terms \( \frac{y^4}{y^6} \), we get \( y^{4 - 6}=y^{-2} \). But we need positive exponents, so \( y^{-2}=\frac{1}{y^2} \).

Step4: Combine all the simplified terms

Multiply the simplified coefficient, \( x \)-term, and \( y \)-term together. So we have \( \frac{5}{2}\times x^3\times\frac{1}{y^2}=\frac{5x^3}{2y^2} \).

Answer:

\( \frac{5x^3}{2y^2} \)