According to exponents rules what is the rational exponents in the equivalent expression to exponent 3 square root 5. Enter in fraction form

Answer 1

The expression "exponent 3 square root 5" can be interpreted as \( (5^{\frac{1}{2}})^3 \).

Using the rule of exponents that states \((a^m)^n = a^{m \cdot n}\), we can rewrite this as:

\[ (5^{\frac{1}{2}})^3 = 5^{\frac{1}{2} \cdot 3} = 5^{\frac{3}{2}} \]

So the expression in terms of rational exponents is:

\[ 5^{\frac{3}{2}} \]

Thus, the rational exponent in fraction form is \(\frac{3}{2}\).