Question

simplify \\(\frac{8x^{0}y^{2}z^{5}}{2y^{2}z^{3}}\\). assume that no denominator equals zero. \\(\frac{8x^{0}y^{2}z^{5}}{2y^{2}z^{3}} = \\) select choice \\(\boldsymbol{\downarrow}\\) select choice \\(4xyz^2\\) \\(4z^2\\) \\(16z^2\\)

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients: $\frac{8}{2} = 4$.

Step2: Simplify the \(x\)-term

For the \(x\)-term, we have \(x^0\). By the zero - exponent rule \(a^0=1\) (\(a
eq0\)), so \(x^0 = 1\).

Step3: Simplify the \(y\)-term

For the \(y\)-terms, we use the quotient rule for exponents \(\frac{a^m}{a^n}=a^{m - n}\) (\(a
eq0\)). Here, \(m = 2\) and \(n = 2\), so \(\frac{y^{2}}{y^{2}}=y^{2-2}=y^{0}=1\) (since \(y
eq0\)).

Step4: Simplify the \(z\)-term

For the \(z\)-terms, using the quotient rule for exponents \(\frac{a^m}{a^n}=a^{m - n}\) (\(a
eq0\)). Here, \(m = 5\) and \(n = 3\), so \(\frac{z^{5}}{z^{3}}=z^{5 - 3}=z^{2}\).

Step5: Multiply the simplified terms

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

Answer:

\(4z^{2}\) (corresponding to the option "4z^2")