Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 438: 83

$x = 5$

$\frac{4x^{3}+5}{8} = 63.125$ $4x^{3} + 5 = 505$ $4x^{3} = 505 - 5$ $4x^{3} = 500$ $x^{3} = 125$ $x = 125^{\frac{1}{3}}$ $x = 5$ Check: $\frac{4x^{3}+5}{8} \overset{?}{=} 63.125$ $\frac{4(5)^{3}+5}{8} \overset{?}{=} 63.125$ $\frac{4(125)+5}{8} \overset{?}{=} 63.125$ $\frac{500+5}{8} \overset{?}{=} 63.125$ $\frac{505}{8} \overset{?}{=} 63.125$ $63.125 = 63.125$