To simplify: The given expression sqrt[3]{frac{54x^{2}y^{4}}{2x^{5}y}}

banganX

banganX

Answered question

2020-11-22

To simplify:
The given expression 3{54x2y42x5y}

Answer & Explanation

au4gsf

au4gsf

Skilled2020-11-23Added 95 answers

Step 1
Properties:
Law of exponents:
For any rational exponent mn in liwest terms, where m and n are integers and n>0, we define
amn=(n{a})m=n{am}
If n is even, then we require that a0.
Step 2
Consider the given expression,
3{54x2y42x5y}=3{27x2y4x5y}
Apply exponent rule: xaxb=xab, we get
3{27x2y4x5y}=3{27x25y41}
=3{27x3y3}
3{27y3x3}
Apply radical rule n{ab}=n{a}n{b} we get
3{27y3}3{x3}
By using the law of exponents,
3{27y3}3{x3}=3{27}3{y3}3{x3}
=(33)13y33x33
=3yx
Final Stetement:
The simplified form of 3{54x2y42x5y} is 3yx

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