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Which expression is equivalent to RootIndex 3 StartRoot StartFraction 75 a Superscript 7 Baseline b Superscript 4 Baseline Over 40 a Superscript 13 Baseline c Superscript 9 Baseline EndFraction EndRoot? Assume a not-equals 0 and c not-equals 0.

A. StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 2 c cubed EndFraction
B. StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a squared c cubed EndFraction
C. StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 6 c cubed EndFraction
D. StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a c EndFraction

User Anbanm
by
8.4k points

2 Answers

6 votes

Answer:

B on edge2020

User IturPablo
by
8.3k points
3 votes

Answer:

B.
(b)/(2a^(2)c^3)\sqrt[3]{15b}

Explanation:

Given:

The expression to simplify is given as:


\sqrt[3]{(75a^7b^4)/(40a^(13)c^9)}

Use the exponent property
(a^m)/(a^n)=a^(m-n)


(a^7)/(a^(13))=a^(7-13)=a^(-6)

Use the exponent property
(a^m)^n=a^(m* n)


a^(-6)=a^(-2* 3)=(a^(-2))^3


b^4=b* b^3\\c^(9)=(c^3)^3

Reducing
(75)/(40) to simplest form, we get:


(5* 5* 3)/(2^3* 5)=(15)/(2^3)

Therefore, expression becomes:


\sqrt[3]{(15(a^(-2))^3* b* b^3)/(2^3(c^3)^3)}

Use the cubic root property:


\sqrt[3]{x^3} =x. Thus, the expression becomes:


(a^(-2)b)/(2c^3)\sqrt[3]{15b}

Using the exponent property
a^(-m)=(1)/(a^m)


a^(-2)=(1)/(a^2)

So, the final expression is:


(b)/(2a^(2)c^3)\sqrt[3]{15b}

Therefore, the correct option is option B.

User Brokendreams
by
8.6k points
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