Question

1. \\(\frac{2y^{0}}{(x^{4}y^{4})^{4} cdot 2x}\\)

Explanation:

Step1: Simplify \( y^0 \) and \( (x^4y^4)^4 \)

Recall that any non - zero number to the power of 0 is 1, so \( y^0 = 1 \).
For \( (x^4y^4)^4 \), use the power of a product rule \((ab)^n=a^n b^n\) and the power of a power rule \((a^m)^n=a^{mn}\).
\((x^4y^4)^4=(x^4)^4(y^4)^4=x^{16}y^{16}\)
The original expression becomes \(\frac{2\times1}{x^{16}y^{16}\cdot2x}\)

Step2: Simplify the denominator

Multiply the terms in the denominator: \(x^{16}y^{16}\cdot2x = 2x^{16 + 1}y^{16}=2x^{17}y^{16}\)
Now the expression is \(\frac{2}{2x^{17}y^{16}}\)

Step3: Simplify the fraction

Cancel out the common factor of 2 in the numerator and the denominator.
\(\frac{2}{2x^{17}y^{16}}=\frac{1}{x^{17}y^{16}}\)

Answer:

\(\frac{1}{x^{17}y^{16}}\)