The given expression using rational exponents. Then simplify and convert back to radical notation. Assume that all variables represent positive real numbers. Given: The expression is displaystylesqrt{{{81}{a}^{12}{b}^{20}}}

allhvasstH

allhvasstH

Answered question

2021-02-05

The given expression using rational exponents. Then simplify and convert back to radical notation. Assume that all variables represent positive real numbers.
Given:
The expression is 81a12b20

Answer & Explanation

wornoutwomanC

wornoutwomanC

Skilled2021-02-06Added 81 answers

Key points used:
- If a is real number and mnis rational number in lowest terms with n>1, then amn=(am)1n=amn provided that an is a real number.
- If a is real number and n is an integer with n2, then a1n=an provided that an exists.
(a,b)r=ar,br
- Power rule (am)n=amn
Calculation:
Consider the expression 81a12b20
Write the expression 81a12b20 using rational exponents.
And we know that amn=(am)1n=amn
81a12b20=(81a12b20)12
From (a,b)r=ar,br,(81a12b20)12=8112(a12)12,(b20)12
8112(a12)12,(b20)12=(92)12(a12)12,(b20)12
And from power rule (am)n=amn we can write (92)12(a12)12,(b20)12 as
(92)12(a12)12,(b20)12=9,a6,b10
Conclusion:
Therefore, 81a12b20=9a6b10.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

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