Question

algebra 2 with probability - x(a) - si
5 - 2: mathxl for school: practice and problem - solving porny
part 4 of 4
justify each step used in
simplifying the expression.
the power of a product property
addition.
the product of powers property
the power of a power property
relating exponents and radicals.
the product property of radicals.
the quotient property of radicals.
subtraction.
the quotient of powers property
the step $(a^{\frac {x}{4}})=a^{\frac {+}{4}}$ is valid
the step $a^{\frac {1}{4}}=\sqrt 4{a}$ is valid by
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Explanation:

Step1: Analyze the first step \((a^{\frac{x}{4}})^{\frac{1}{x}}=a^{\frac{1}{4}}\)

By the Power of a Power Property \((a^{m})^{n}=a^{mn}\), here \(m = \frac{x}{4}\) and \(n=\frac{1}{x}\), so \(a^{\frac{x}{4}\times\frac{1}{x}}=a^{\frac{1}{4}}\)

Step2: Analyze the second step \(a^{\frac{1}{4}}=\sqrt[4]{a}\)

By the rule of relating exponents and radicals \(a^{\frac{1}{n}}=\sqrt[n]{a}\), here \(n = 4\)

Answer:

The step \((a^{\frac{x}{4}})^{\frac{1}{x}}=a^{\frac{1}{4}}\) is valid by the Power of a Power Property. The step \(a^{\frac{1}{4}}=\sqrt[4]{a}\) is valid by relating exponents and radicals.