Question

question
fully simplify using only positive exponents.
\frac{20x^{5}y^{8}}{8x^{4}y^{4}}
answer attempt 1 out of 2

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \( \frac{20}{8} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 4. So \( \frac{20\div4}{8\div4}=\frac{5}{2} \).

Step2: Simplify the \( x \)-terms

For the \( x \)-terms, we use the rule of exponents \( \frac{x^m}{x^n}=x^{m - n} \). Here, \( m = 5 \) and \( n = 4 \), so \( \frac{x^5}{x^4}=x^{5 - 4}=x^1=x \).

Step3: Simplify the \( y \)-terms

For the \( y \)-terms, we use the same rule of exponents \( \frac{y^m}{y^n}=y^{m - n} \). Here, \( m = 8 \) and \( n = 4 \), so \( \frac{y^8}{y^4}=y^{8 - 4}=y^4 \).

Step4: Combine the simplified terms

Multiply the simplified coefficient, \( x \)-term, and \( y \)-term together. So we have \( \frac{5}{2}\times x\times y^4=\frac{5}{2}xy^4 \).

Answer:

\( \frac{5}{2}xy^4 \)