Questions: Simplify. u^(2/3) * u^(2/5) Assume that the variable represents a

Solution Steps

To simplify the expression \( u^{\frac{2}{3}} \cdot u^{\frac{2}{5}} \), we can use the property of exponents that states when multiplying like bases, we add the exponents. Therefore, we need to add the exponents \(\frac{2}{3}\) and \(\frac{2}{5}\).

We start with the expression \( u^{\frac{2}{3}} \cdot u^{\frac{2}{5}} \).

Using the property of exponents that states \( a^m \cdot a^n = a^{m+n} \), we can combine the exponents: \[ u^{\frac{2}{3}} \cdot u^{\frac{2}{5}} = u^{\frac{2}{3} + \frac{2}{5}} \]

To add the fractions \( \frac{2}{3} \) and \( \frac{2}{5} \), we find a common denominator. The least common multiple of 3 and 5 is 15. Thus, we convert the fractions: \[ \frac{2}{3} = \frac{10}{15}, \quad \frac{2}{5} = \frac{6}{15} \] Now, we can add them: \[ \frac{10}{15} + \frac{6}{15} = \frac{16}{15} \]

Substituting back, we have: \[ u^{\frac{2}{3}} \cdot u^{\frac{2}{5}} = u^{\frac{16}{15}} \]

Final Answer