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))

Express Fifth Root of y: To find the equivalent exponential expression for (root(5)(y))^(4), we need to express the fifth root of y as y raised to a power. The fifth root of y can be written as y^(1/5).Apply Power to Power Rule: Now, we need to apply the power to a power rule, which states that (a^(m))^n = a^(m*n). Here, we have (y^(1/5))^4, which means we need to multiply the exponents.Multiply Exponents: Multiplying the exponents, we get y^((1/5)*4) = y^(4/5). This simplifies to y^(4/5).Match Answer Choice: Looking at the answer choices, we can see that y^(4/5) matches option (A). Therefore, the equivalent exponential expression is y^((4)/(5)).

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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 $(\sqrt[5]{y})^{4}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $y^{\frac{4}{5}}$ $\newline$ (B) $y^{\frac{5}{4}}$ $\newline$ (C) $\frac{y^{5}}{y^{4}}$ $\newline$ (D) $\frac{y^{4}}{y^{5}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which exponential expression is equivalent to

(\sqrt[5]{y})^{4}

\newline

Choose

1

answer:

\newline

(A)

y^{\frac{4}{5}}

\newline

(B)

y^{\frac{5}{4}}

\newline

(C)

\frac{y^{5}}{y^{4}}

\newline

(D)

\frac{y^{4}}{y^{5}}

Express Fifth Root of y: To find the equivalent exponential expression for $(\sqrt[5]{y})^{4}$ , we need to express the fifth root of y as y raised to a power. $\newline$ The fifth root of y can be written as $y^{\frac{1}{5}}$ .
Apply Power to Power Rule: Now, we need to apply the power to a power rule, which states that $(a^{m})^{n} = a^{m*n}$ . Here, we have $(y^{\frac{1}{5}})^{4}$ , which means we need to multiply the exponents.
Multiply Exponents: Multiplying the exponents, we get $y^{(\frac{1}{5})\cdot 4} = y^{\frac{4}{5}}$ . $\newline$ This simplifies to $y^{\frac{4}{5}}$ .
Match Answer Choice: Looking at the answer choices, we can see that $y^{(4/5)}$ matches option (A). $\newline$ Therefore, the equivalent exponential expression is $y^{\left(\frac{4}{5}\right)}$ .