Mathematics

Mathematics

Problem

Write each expression in exponential form. (10)3(\sqrt{10})^3
Intuitive explanation

You're converting a radical expression into exponential form—the key is recognizing that a square root is really a fractional exponent. Since 10=101/2\sqrt{10} = 10^{1/2}, you can apply the power rule (am)n=amn(a^m)^n = a^{mn} to combine the exponents. This transforms any radical into clean exponential notation.

Intuitive explanation

You're converting a radical expression into exponential form—the key is recognizing that a square root is really a fractional exponent. Since 10=101/2\sqrt{10} = 10^{1/2}, you can apply the power rule (am)n=amn(a^m)^n = a^{mn} to combine the exponents. This transforms any radical into clean exponential notation.

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