Answer:
See explanation
Step-by-step explanation:
The given expression is: [tex](24)^{\frac{1}{3}}[/tex]
Recall that 24=3*8
[tex]\implies(24)^{\frac{1}{3}}=(8*3)^{\frac{1}{3}}[/tex]
Recall again that:
[tex](a*b)^n=a^n*b^n[/tex]
[tex]\implies (8*3)^{\frac{1}{3}}=(8)^{\frac{1}{3}}*(3)^{\frac{1}{3}}[/tex]
[tex]\implies (8*3)^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}*(3)^{\frac{1}{3}}[/tex]
[tex]\implies (8*3)^{\frac{1}{3}}=2^{3*\frac{1}{3}}*(3)^{\frac{1}{3}}[/tex]
[tex]\implies (8*3)^{\frac{1}{3}}=2*(3)^{\frac{1}{3}}[/tex]
We rewrite in radical form to obtain
[tex]\implies (8*3)^{\frac{1}{3}}=2\sqrt[3]{3}[/tex]
Answer:
[tex]24^{1/3}[/tex] = [tex]\sqrt[3]{24}[/tex] or [tex]2\sqrt[3]{3}[/tex]
Step-by-step explanation:
We will apply one of the laws of indices which states
[tex]a^{b/c}[/tex] = [tex]\sqrt[c]({a})^b[/tex]
So from the question given, 24 superscript one-third = [tex]24^{1/3}[/tex]
by comparison, a= 24, b = 1, and c = 3
Applying the law I stated above
[tex]a^{b/c}[/tex] = [tex]\sqrt[c]({a})^b[/tex]
[tex]a^{b/c}[/tex] = [tex]24^{1/3}[/tex] = [tex]\sqrt[3]({24})^{1}[/tex]
[tex]a^{b/c}[/tex] = [tex]\sqrt[3]({8 X 3})^{1}[/tex]
[tex]a^{b/c}[/tex] = [tex]\sqrt[3]({8})^{1}[/tex] × [tex]\sqrt[3]({3})^{1}[/tex]
[tex]a^{b/c}[/tex] = 2 × [tex]\sqrt[3]({3})^{1}[/tex]
[tex]2\sqrt[3]{3}[/tex] (superscript 1 is removed because any value raised to the power of one is equal to that value) or [tex]\sqrt[3]{24}[/tex]
Therefore the expression will be [tex]2\sqrt[3]{3}[/tex] or [tex]\sqrt[3]{24}[/tex] ---- Answer
