Answer:
(a.) 27^4/3 = 81, (b.) 36^3/2 = 216, (c.) (1/8)^2/3 = 1/4, (d.) 128^5/7 = 32
Step-by-step explanation:
All these expressions can be converted in square roots.
In order to do this, we can picture the fractional exponents as exponent / index
(a.) So for this first problem, we would have the cube root of [tex]27^{\frac{4}{3} }[/tex] or
[tex]\sqrt[3]{(27)^{4} }[/tex].
We must do the equation inside the radical first (i.e., [tex](27)^{4}[/tex]) to get [tex]\sqrt[3]{531,441}[/tex] = 81
We can follow these same steps for the remaining equations:
(b.) [tex]36^{\frac{3}{2} }[/tex] = [tex]\sqrt{(36)^3}[/tex] = [tex]\sqrt{46,656}[/tex] = 216
(c.) [tex](\frac{1}{8})^\frac{2}{3}[/tex] = [tex]\sqrt[3]{(\frac{1}{8})^{2} }[/tex] = [tex]\sqrt[3]{(\frac{1^2}{8^2}) }[/tex] = [tex]\sqrt[3]{(\frac{1}{64}) }[/tex] = [tex]\frac{1}{4}[/tex]
(d.) [tex]128^{\frac{5}{7} }[/tex] = [tex]\sqrt[7]{(128)^{5} }[/tex] = 32