The simplified form of the expression displaystyle{sqrt[{{4}}]{{{c}{d}^{2}}}}times{sqrt[{{3}}]{{{c}^{2}{d}}}}.

Khaleesi Herbert 2021-01-05 Answered
The simplified form of the expression
cd24×c2d3.
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Expert Answer

grbavit
Answered 2021-01-06 Author has 109 answers
Formula used:
Product property of radicals:
If a and b are real numbers and n > 1 is an integer, the product property is true provided that the radicals are real numbers.
an×bn=abn
If m and n are integers and n > 1 is an integer, then
amn=amn
Calculation:
Consider the expression,
cd24×c2d3
Rewrite the provided expression as rational exponents.
cd24×c2d3=(cd2)1/4×(c2d)1/3
Use the product property.
(cd2)1/4×(c2d)1/3=(c)1/4×(d2)1/4×(c2)1/3×(d)1/3
Use the formula amn=am/n and simplify the expression.
(c)1/4×(d2)1/4×(c2)1/3×(d)1/3=c1/4×d2/4×c2/3×d1/3
Add the powers of the same bases.
c1/4×d2/4×c2/3×d1/3=c(14)+(24)×d(24)+(13)
=c1112×d1012
The obtained expression with rational exponents can be rewritten into radicals as,
=c1112×d1012=(c11)112×(d10)112
=c11d1012
Answer: cd24×c2d3isc11d1012
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Jeffrey Jordon
Answered 2021-10-26 Author has 2047 answers

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