Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 386: 53

$64$

Note that" $16^{1.5}=16^{\frac{3}{2}}$ Since $2^4=16$, then: $16^{\frac{3}{2}}=(2^4)^{\frac{3}{2}}$ Now, recall the basic exponent property (pg. 360): $(a^m)^n=a^{mn}$ Applying this property, we get: \begin{align*} (2^4)^{\frac{3}{2}}&=2^{\frac{4\cdot 3}{2}}\\ &=2^{\frac{12}{2}}\\ &=2^{6}\\ &=64 \end{align*}