Answer the following questions related to nth roots and rational exponents.

MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number

Problem

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

a>0

and positive integers

m

and

n

, the equality

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

holds. (iii) Rewrite

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

in exponential form and

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

in radical form.

Related theory

Real Number System
Laws of Exponents

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