Question

fully simplify using only positive exponents.\\(\frac{7x^{4}y^{7}}{35xy}\\)

Explanation:

Step1: Simplify the coefficients

First, simplify the fraction of the coefficients \( \frac{7}{35} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 7. So, \( \frac{7\div7}{35\div7}=\frac{1}{5} \).

Step2: Simplify the \( x \)-terms

For the \( x \)-terms, we use the quotient rule of exponents, which states that \( \frac{x^m}{x^n}=x^{m - n} \) (where \( x
eq0 \), \( m \) and \( n \) are real numbers). Here, we have \( \frac{x^4}{x^1} \), so applying the rule, we get \( x^{4 - 1}=x^3 \).

Step3: Simplify the \( y \)-terms

For the \( y \)-terms, we also use the quotient rule of exponents. We have \( \frac{y^7}{y^1} \), so applying the rule \( \frac{y^m}{y^n}=y^{m - n} \), we get \( y^{7 - 1}=y^6 \).

Step4: Combine the simplified terms

Now, we combine the simplified coefficient, \( x \)-term, and \( y \)-term. So, putting it all together, we have \( \frac{1}{5}\times x^3\times y^6=\frac{x^3y^6}{5} \).

Answer:

\( \frac{x^3y^6}{5} \)