Simplify the 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

Solution:

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

We can write it as √5 × 5^1/3

We know the property of exponents, a^m × aⁿ = a^{m + n}

5^1/2 × 5^1/3 = 5^{1/2 + 1/3}

5^1/2 × 5^1/3 = 5^{(2 + 3)/6}

5^1/2 × 5^1/3 = 5^5/6

Therefore, it is simplified as 5 to the power of 5 over 6.

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

Summary:

The simplified form of the square root of 5 multiplied by the cube root of 5 is 5 to the power of 5 over 6.