Mathematics

Problem

Answer the following questions related to nth roots and rational exponents. a. (i) State the definition of the nth root of a positive real number. b. (ii) Explain why, for

a>0

and positive integers

m

and

n

, the equality

a^{\frac{m}{n}} = \sqrt[n]{a^{m}}

holds. c. (iii) Rewrite

\sqrt[5]{x^{3}}

in exponential form and

y^{\frac{3}{4}}

in radical form.

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