Question

question
fully simplify using only positive exponents.
\\(\frac{4x^{4}y^{7}}{2x^{8}y^{7}}\\)
answer attempt 1 out of 2

Explanation:

Step1: Simplify the coefficient

Divide the coefficient 4 by 2.
$\frac{4}{2} = 2$

Step2: Simplify the \(x\)-terms using exponent rule \( \frac{a^m}{a^n} = a^{m - n} \)

For the \(x\)-terms, we have \( \frac{x^4}{x^8} = x^{4 - 8} = x^{-4} \). But we need positive exponents, so \( x^{-4} = \frac{1}{x^4} \)

Step3: Simplify the \(y\)-terms using exponent rule \( \frac{a^m}{a^n} = a^{m - n} \)

For the \(y\)-terms, \( \frac{y^7}{y^7} = y^{7 - 7} = y^0 = 1 \) (since any non - zero number to the power of 0 is 1)

Step4: Combine the results

Multiply the coefficient, the simplified \(x\)-term, and the simplified \(y\)-term.
\( 2\times\frac{1}{x^4}\times1=\frac{2}{x^4} \)

Answer:

\(\frac{2}{x^{4}}\)