Questions: Simplify. x^(5/8) * x^(3/4) Assume that the variable represents a positive real number.

Solution Steps

To simplify the expression \(x^{\frac{5}{8}} \cdot x^{\frac{3}{4}}\), we can use the product rule for exponents, which states that when multiplying two powers with the same base, we add the exponents.

To simplify the expression \(x^{\frac{5}{8}} \cdot x^{\frac{3}{4}}\), we use the product rule for exponents, which states that when multiplying two powers with the same base, we add the exponents:

\[ x^{\frac{5}{8}} \cdot x^{\frac{3}{4}} = x^{\frac{5}{8} + \frac{3}{4}} \]

To add the fractions \(\frac{5}{8}\) and \(\frac{3}{4}\), we need a common denominator. The least common multiple of 8 and 4 is 8. We can rewrite \(\frac{3}{4}\) as \(\frac{6}{8}\):

\[ \frac{3}{4} = \frac{6}{8} \]

Now we can add the two fractions:

\[ \frac{5}{8} + \frac{6}{8} = \frac{11}{8} \]

Thus, we have:

\[ x^{\frac{5}{8}} \cdot x^{\frac{3}{4}} = x^{\frac{11}{8}} \]

Final Answer