Radicals and Exponents Simplify the expression. frac{x^{4}(3x)^{2}}{x^{3}}

Tabansi 2020-10-18 Answered
Radicals and Exponents Simplify the expression.
x4(3x)2x3
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Expert Answer

Bentley Leach
Answered 2020-10-19 Author has 109 answers

Procedure used:
The definition of a Rational Exponent is,
For any rational exponent m/n in lowest, where m and n are integers and n>0, we define
am/n=(an)m or equivalently am/n=anm
If n is even, then we require that a0.
a=b means b2=a and b 0
This implies that b=a12 and therefore
a=a12
According to the Zero and Negative Exponents rule, we can see that if aq0 is a real number and n is a positive integer, then
a0=1 and an=1an
From, the law of exponents, we know that
(ab)m=ambm.....(1)
aman=am+n.....(2)
aman=amn.....(3)
Calculation:
Using the Law of Exponents (1), (2) and (3), we get that
x4(3x)2x3=x4(32x2)x3
=32x4+2x3
=32x6x3
=9x63
=9x3
Answer:
The simplified form of the expression, x4(3x)2x3=9x3

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Jeffrey Jordon
Answered 2021-10-27 Author has 2313 answers

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