Question

(\frac{3^{\frac{7}{4}}}{3^{\frac{1}{4}}})

Explanation:

Step1: Use exponent division rule

When dividing exponents with the same base \( a^m \div a^n = a^{m - n} \), here base is 3, so \( 3^{\frac{7}{4}} \div 3^{\frac{1}{4}} = 3^{\frac{7}{4}-\frac{1}{4}} \)

Step2: Subtract the exponents

Calculate \( \frac{7}{4}-\frac{1}{4}=\frac{7 - 1}{4}=\frac{6}{4}=\frac{3}{2} \)

Step3: Simplify the result

\( 3^{\frac{3}{2}}=\sqrt{3^3}=\sqrt{27} = 3\sqrt{3}\) or as \( 3^{1.5}\)

Answer:

\( 3^{\frac{3}{2}} \) (or \( 3\sqrt{3} \), or approximately \( 5.196 \))