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(y+y^(2))/(y^(-(2)/(3)))
Which of the following expressions is equivalent to the given expression assuming
y is nonzero?
Choose 1 answer:
(A)
y^(-(3)/(2))+y^(-3)
(B)
y^((3)/(2))+y^(3)
(C)
y^((1)/(3))+y^((4)/(3))
(D)
y^((5)/(3))+y^((8)/(3))

$\frac{y+y^{2}}{y^{-\frac{2}{3}}}$ $\newline$ Which of the following expressions is equivalent to the given expression assuming $y$ is nonzero? $\newline$ Choose $1$ answer: $\newline$ (A) $y^{-\frac{3}{2}}+y^{-3}$ $\newline$ (B) $y^{\frac{3}{2}}+y^{3}$ $\newline$ (C) $y^{\frac{1}{3}}+y^{\frac{4}{3}}$ $\newline$ (D) $y^{\frac{5}{3}}+y^{\frac{8}{3}}$

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Compare linear, exponential, and quadratic growth

Full solution

Q.

\frac{y+y^{2}}{y^{-\frac{2}{3}}}

\newline

Which of the following expressions is equivalent to the given expression assuming

y

is nonzero?

\newline

Choose

1

answer:

\newline

(A)

y^{-\frac{3}{2}}+y^{-3}

\newline

(B)

y^{\frac{3}{2}}+y^{3}

\newline

(C)

y^{\frac{1}{3}}+y^{\frac{4}{3}}

\newline

(D)

y^{\frac{5}{3}}+y^{\frac{8}{3}}

Multiply by $y^{\frac{2}{3}}$ : Simplify the given expression by multiplying both the numerator and the denominator by $y^{\frac{2}{3}}$ to eliminate the negative exponent in the denominator. $\newline$ Given expression: $\frac{y + y^2}{y^{-\left(\frac{2}{3}\right)}}$ $\newline$ Multiply numerator and denominator by $y^{\frac{2}{3}}$ : $\frac{y \cdot y^{\frac{2}{3}} + y^2 \cdot y^{\frac{2}{3}}}{y^{-\left(\frac{2}{3}\right)} \cdot y^{\frac{2}{3}}}$
Apply laws of exponents: Apply the laws of exponents to simplify the expression further. $\newline$ When multiplying like bases, we add the exponents: $y^{(1 + \frac{2}{3})} + y^{(2 + \frac{2}{3})}$ $\newline$ Simplify the exponents: $y^{(\frac{3}{3} + \frac{2}{3})} + y^{(\frac{6}{3} + \frac{2}{3})}$
Perform addition of exponents: Perform the addition of the exponents. $y^{\frac{5}{3}} + y^{\frac{8}{3}}$
Match with answer choices: Match the simplified expression with the given answer choices. $\newline$ The simplified expression is $y^{\frac{5}{3}} + y^{\frac{8}{3}}$ , which corresponds to answer choice (D).

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\newline

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