Evaluate 8^5/3

[mkxc3]

what is a simple way to solve it?

 

[pka]

\(\displaystyle {\Large{8^{\frac{5}{3}}} = {\left( {{2^3}} \right)^{\frac{5}{3}}} = ?}\)

 

[mkxc3]

\(\displaystyle {\Large{8^{\frac{5}{3}}} = {\left( {{2^3}} \right)^{\frac{5}{3}}} = ?}\)

ah, yes! what if it was a 7 instead of an 8? would you still be able to use this, or a similar method?

 

[Dr.Peterson]

You'd use a calculator. (Or you'd do the cube root by hand.)

But please note that 8^5/3 doesn't mean [MATH]8^{\frac{5}{3}}[/MATH]; it means [MATH]\frac{8^5}{3}[/MATH]. You meant to write 8^(5/3).

 

[pka]

ah, yes! what if it was a 7 instead of an 8? would you still be able to use this, or a similar method?

\(\displaystyle {\Large 7^{\frac{5}{3}}}\) As you know \(\displaystyle \dfrac{5}{3}=1+\frac{2}{3}\)
Thus \(\displaystyle {\Large 7^{\frac{5}{3}}=7^1\sqrt[3]{7^2}=7\sqrt[3]{7^2}}\).

 

[Steven G]

what is a simple way to solve it?

8^5/3 ask you a couple of questions. What times itself 3 times equals 8? That answer is 2. Then ask yourself what is 2 raised to the 5th power, or if you prefer what is 2⁵?

If you do not know what times itself equals the base maybe because the base is 7, then you leave the cube root.
For example: simplify 2^3/2. Since I do not know a (nice) answer to that, then I do the power next. What is 2^3? The answer is 8, so I will leave my answer as sqrt(8)