Consider the two numbers and

MATHEMATICS · Subjective · CBSE · Mathematics · Number Systems · Number Systems

Problem

Consider the two numbers 232^{\sqrt{3}} and 32\sqrt{3^{2}}. Answer the following: (i) Rewrite each number so that no radical sign appears in the exponent. (ii) Without using a calculator, determine which number is greater. (iii) Give a clear reason for your conclusion, quoting the relevant law of exponents.

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