Express the radical as power. (a) root(6)(x^5) (b) sqrt(x)^9

SchachtN 2020-11-05 Answered

Express the radical as power.
(a)x56
To simplify:
The expression x56 and express the answer using rational exponents.
(b) (x)9
To simplify:
The expression (x)9 and express the answer using rational exponents.

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Expert Answer

Velsenw
Answered 2020-11-06 Author has 91 answers

(a) Concept used:
If ais a real number, n is a positive integer and amn is a real number then the rational exponent expression amn is equivalent to radical expression amn.
The above statement can be expressed as,
anm=amn ...... (1)
Calculation:
The given expression is x56
Subtitute 6 for n, 5 for m and x for a in the equation (1) to obtain the equialent expression in rational exponent as,
x56=(x16)5
=x56
Conclusion:
Thus, the equvalent expression of the expression x56 is x56.
(b) Calculation:
The given expression is (x)9
Subtitute 2 for n, 9 for m and x for a in the equation (1) to obtain the equialent expression in rational exponent as,
(x)9=(x12)9
=x92
Conclusion:
Thus, the equivalent expression of the expression (x)9 is x92.

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