Question

Simplify square root of 5 multiplied by the cube root of 5.

5 to the power of 5 over 6
5 to the power of 1 over 6
5 to the power of 2 over 3
5 to the power of 7 over 6

Answer 1

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.

• The expression is:

$(\sqrt{5}).(\sqrt[3]{5})$

• 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.