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(bd)^((1)/(4))*((b)/(d))^(4)
Which of the following expressions is equivalent to the given expression assuming
d is nonzero?
Choose 1 answer:
(A)
b^((17)/(4))d^((17)/(4))
(B)
b^((17)/(4))d^(-(15)/(4))
(c)
b^(2)
(D)
(b)/(d)

$(b d)^{\frac{1}{4}} \cdot\left(\frac{b}{d}\right)^{4}$ $\newline$ Which of the following expressions is equivalent to the given expression assuming $d$ is nonzero? $\newline$ Choose $1$ answer: $\newline$ (A) $b^{\frac{17}{4}} d^{\frac{17}{4}}$ $\newline$ (B) $b^{\frac{17}{4}} d^{-\frac{15}{4}}$ $\newline$ (C) $b^{2}$ $\newline$ (D) $\frac{b}{d}$

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Compare linear and exponential growth

Full solution

Q.

(b d)^{\frac{1}{4}} \cdot\left(\frac{b}{d}\right)^{4}

\newline

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

d

is nonzero?

\newline

Choose

1

answer:

\newline

(A)

b^{\frac{17}{4}} d^{\frac{17}{4}}

\newline

(B)

b^{\frac{17}{4}} d^{-\frac{15}{4}}

\newline

(C)

b^{2}

\newline

(D)

\frac{b}{d}

Simplify expression using exponents: Simplify the expression by applying the properties of exponents. $\newline$ $(bd)^{\frac{1}{4}}\cdot\left(\frac{b}{d}\right)^{4}$ can be rewritten as $\left(b^{\frac{1}{4}} \cdot d^{\frac{1}{4}}\right) \cdot \left(\frac{b^{4}}{d^{4}}\right)$ .
Separate terms involving $b$ and $d$ : Separate the terms involving $b$ and $d$ . $\newline$ This gives us $b^{$ $1$ / $4$ } \cdot b^ $4$ / d^{ $1$ / $4$ } \cdot d^ $4$ .
Combine exponents for $b$ and $d$ : Combine the exponents for $b$ and $d$ using the property of exponents that states $a^{m} \cdot a^{n} = a^{m+n}$ . $\newline$ For $b$ , we have $b^{$ $1$ / $4$ + $4$ } = b^{ $1$ / $4$ + $16$ / $4$ } = b^{ $17$ / $4$ }. $\newline$ For $d$ , we have $d^{$ $1$ / $4$ - $4$ } = d^{ $1$ / $4$ - $16$ / $4$ } = d^{ $-15$ / $4$ }.
Write final expression: Write the final expression. $\newline$ The equivalent expression is $b^{\frac{17}{4}} \cdot d^{-\frac{15}{4}}$ .

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