Answer:
5 to the power of 5 over 6 = \(5^{\frac{5}{6}}\)
Step-by-step explanation:
1)Let's define some properties about exponent:
\(a^{\frac{b}{c}}=\sqrt[c]{a^{b}}\)
For example :
\(4^{\frac{1}{2}}=\sqrt[2]{4^{1}}=\sqrt[2]{4}=\sqrt{4}=2\)
\(2^{\frac{6}{3}}=\sqrt[3]{2^{6}}=\sqrt[3]{64}=4\)
2)Another property of exponent is :
\((a^{b}).(a^{c})=a^{b+c}\)
For example :
\((4^{2}).(4^{3})=4^{2+3}=4^{5}=1024\)
This means that when we have two exponential functions with the same base that are multiplying between them, we can sum the exponents in order to make a new exponential function with the same base.
Using this two properties we can solve the problem.
\((\sqrt{5}).(\sqrt[3]{5})\)
- Using the two properties :
\((\sqrt{5}).(\sqrt[3]{5})=(5^{\frac{1}{2}}).(5^{\frac{1}{3}})=5^{\frac{1}{2}+\frac{1}{3}}\)
Now, \(\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\)
Therefore, the final expression is
\(5^{\frac{1}{2}+\frac{1}{3}}=5^{\frac{5}{6}}\) ⇒
\((\sqrt{5}).(\sqrt[3]{5})=5^{\frac{5}{6}}\)
The correct answer is :
5 to the power of 5 over 6.
