To calculate: The simplified value of the radical expression displaystylesqrt{{{18}{a}}}divsqrt{{{2}{a}^{4}}}.

Dolly Robinson 2020-11-14 Answered
To calculate: The simplified value of the radical expression 18a÷2a4.
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Expert Answer

unett
Answered 2020-11-15 Author has 119 answers
Given expression is 18a÷2a4.
Formula used:
The product rule for radicals,
anb=anbn
Here, n is the positive integer and a and b are real number.
The relation between radical and rational exponent notation is expressed as,
an=a1/n.
Here, a is the radicand, and n is the index of the radical.
Calculation:
Consider the given expression,
18a÷2a4.
Use the product rule for radicals to simplify the expression,
18a÷2a4=18a2a4
=92a2a2a2
=322a2a2a2
Use the relation between radical and rational exponent notation to simplify the expression,
18a÷2a4=(32)1/2a(a2)1/2(a2)1/2
=(3)2(1/2)a(a)2(1/2)(a)2(1/2)
=(3)a(a)(a)
=3an2
Hence, the simplified value of the provided expression is 3aa2.
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Jeffrey Jordon
Answered 2021-10-25 Author has 2064 answers

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