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Which exponential expression is equivalent to (root(5)(y))^(4) ? Choose 1 answer: (A) y^((4)/(5)) (B) y^((5)/(4)) (C) (y^(5))/(y^(4)) (D) (y^(4))/(y^(5))

Which exponential expression is equivalent to (y5)4 (\sqrt[5]{y})^{4} ?\newlineChoose 11 answer:\newline(A) y45 y^{\frac{4}{5}} \newline(B) y54 y^{\frac{5}{4}} \newline(C) y5y4 \frac{y^{5}}{y^{4}} \newline(D) y4y5 \frac{y^{4}}{y^{5}}

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Full solution

Q. Which exponential expression is equivalent to (y5)4 (\sqrt[5]{y})^{4} ?\newlineChoose 11 answer:\newline(A) y45 y^{\frac{4}{5}} \newline(B) y54 y^{\frac{5}{4}} \newline(C) y5y4 \frac{y^{5}}{y^{4}} \newline(D) y4y5 \frac{y^{4}}{y^{5}}
  1. Express Fifth Root of y: To find the equivalent exponential expression for (y5)4(\sqrt[5]{y})^{4}, we need to express the fifth root of y as y raised to a power.\newlineThe fifth root of y can be written as y15y^{\frac{1}{5}}.
  2. Apply Power to Power Rule: Now, we need to apply the power to a power rule, which states that (am)n=am∗n(a^{m})^{n} = a^{m*n}. Here, we have (y15)4(y^{\frac{1}{5}})^{4}, which means we need to multiply the exponents.
  3. Multiply Exponents: Multiplying the exponents, we get y(15)⋅4=y45y^{(\frac{1}{5})\cdot 4} = y^{\frac{4}{5}}.\newlineThis simplifies to y45y^{\frac{4}{5}}.
  4. Match Answer Choice: Looking at the answer choices, we can see that y(4/5)y^{(4/5)} matches option (A).\newlineTherefore, the equivalent exponential expression is y(45)y^{\left(\frac{4}{5}\right)}.

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