Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 386: 54

$1000$

Note that: $(10000)^{0.75}=(10000)^{\frac{3}{4}}$ Since $10^4=10000$, then: $(10000)^{\frac{3}{4}}=(10^4)^{\frac{3}{4}}$ Now, recall the basic exponent property (pg. 360): $(a^m)^n=a^{mn}$ Applying this property, we get: \begin{align*} (10^4)^{\frac{3}{4}}&=10^{\frac{4\cdot 3}{4}}\\ &=10^{\frac{12}{4}}\\ &=10^{3}\\ &=1000 \end{align*}