To determine: To calculate: a) The indicated operation sqrt[4]{cd}cdotsqrt[5]{c^{2}} b) The indicated operation sqrt[4]{ysqrt[3]{y}} c) The indicated operation sqrt[5]{x}+sqrt[5]{y}+sqrt[4]{x}

Ava-May Nelson

Ava-May Nelson

Answered question

2021-02-11

To determine:
To calculate:
a) The indicated operation 4{cd}5{c2}
b) The indicated operation 4{y3{y}}
c) The indicated operation 5{x}+5{y}+4{x}

Answer & Explanation

SoosteethicU

SoosteethicU

Skilled2021-02-12Added 102 answers

Step 1 a) Formula Given: am an=am+n
Consider the given expression 4{cd}5{c2}
Rewrite the expression with rational exponents
4{cd}5{c2}
=(cd(cd))
=c14 d14 c25
Combine the like bases and use the property am an=am+n
c14 d14 c25
=c14+25 d14
=20{c13d5}
Therefore, the value of 4{cd}5{c2} is 20{c13d5}
Step 2
b) Formula Given: (am)n=amn
am an=am+n
Consider the given expression 4{y3{y}}
Rewrite the expression with rational exponents
4{y3{y}}
=({.}y
Use the property am an=am+n to get,
=(y43)14
Use the property (am)n=amn to get,
=y13
=3{y}
Therefore, the value of 4{y3{y}} is 3{y}
Step 3

 c) Consider the given expression 5{x}+5{y}+4{x}
The given expression is already in simplified form as radicals are not like radicals.
The first two terms have different indices and the first and third terms have different radicands.
Therefore, the value of 5{x}+5{y}+4{x} is

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