.1) 3. Simplify the expression: (5^(3)/(4))^(4)/(3)

To simplify the expression \((5^{\frac{3}{4}})^{\frac{4}{3}}\), we can use the property of exponents that states \((a^m)^n = a^{m \cdot n}\).<br /><br />Given:<br />\[<br />(5^{\frac{3}{4}})^{\frac{4}{3}}<br />\]<br /><br />We apply the property:<br />\[<br />(5^{\frac{3}{4}})^{\frac{4}{3}} = 5^{\frac{3}{4} \cdot \frac{4}{3}}<br />\]<br /><br />Next, we multiply the exponents:<br />\[<br />\frac{3}{4} \cdot \frac{4}{3} = \frac{3 \cdot 4}{4 \cdot 3} = \frac{12}{12} = 1<br />\]<br /><br />So, we have:<br />\[<br />5^{\frac{3}{4} \cdot \frac{4}{3}} = 5^1 = 5<br />\]<br /><br />Therefore, the simplified expression is:<br />\[<br />5<br />\]