Question

question
fully simplify using only positive exponents.
\\(\frac{3x^4y^5}{15x^3y^2}\\)
answer attempt 1 out of 5

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients \( \frac{3}{15} \). We know that \( \frac{3}{15}=\frac{1}{5} \) since both numerator and denominator are divisible by 3.

Step2: Simplify \( x \)-terms

For the \( x \)-terms, we use the rule of exponents \( \frac{x^m}{x^n}=x^{m - n} \). Here, \( m = 4 \) and \( n = 3 \), so \( \frac{x^4}{x^3}=x^{4-3}=x^1=x \).

Step3: Simplify \( y \)-terms

For the \( y \)-terms, we use the same exponent rule \( \frac{y^m}{y^n}=y^{m - n} \). Here, \( m = 5 \) and \( n = 2 \), so \( \frac{y^5}{y^2}=y^{5 - 2}=y^3 \).

Step4: Combine all simplified terms

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

Answer:

\( \frac{xy^3}{5} \)