Question

(xy^3)^4 =
○ xy^12
○ (x^4)y^12
○ xy^7
○ (x^4)y^7
question 6
1 pts
x^0
○ -x
○ x
○ 1
○ 0

Explanation:

First Question ( \((xy^3)^4 =\) )

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((xy^3)^4\), we can apply this rule:
\((xy^3)^4 = x^4 (y^3)^4\)

Step2: Apply power of a power rule

The power of a power rule states that \((a^m)^n = a^{m\times n}\). For \((y^3)^4\), we have:
\((y^3)^4 = y^{3\times4} = y^{12}\)

Step3: Combine the results

From Step1 and Step2, we get \((xy^3)^4 = x^4 y^{12}\) (which is \((x^4)y^{12}\) in the given option format)

By the zero - exponent rule, any non - zero number (or variable, as long as \(x
eq0\)) raised to the power of 0 is equal to 1. That is, for \(x
eq0\), \(x^0 = 1\).

Answer:

\((x^4)y^{12}\) (corresponding to the option: \((x^4)y^{12}\))

Second Question ( \(x^0\) )