Question

question
fully simplify using only positive exponents.
\\(\frac{27x^8y^5}{9x^4y^5}\\)

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients \( \frac{27}{9} \).
\( \frac{27}{9} = 3 \)

Step2: Simplify the \( x \)-terms

Use the quotient rule for exponents \( \frac{a^m}{a^n}=a^{m - n} \) for \( x \)-terms \( \frac{x^8}{x^4} \).
\( \frac{x^8}{x^4}=x^{8 - 4}=x^4 \)

Step3: Simplify the \( y \)-terms

Use the quotient rule for exponents \( \frac{a^m}{a^n}=a^{m - n} \) for \( y \)-terms \( \frac{y^5}{y^5} \).
\( \frac{y^5}{y^5}=y^{5 - 5}=y^0 = 1 \) (since any non - zero number to the power of 0 is 1)

Step4: Multiply the simplified terms

Multiply the results from Step 1, Step 2 and Step 3: \( 3\times x^4\times1 = 3x^4 \)

Answer:

\( 3x^4 \)