Simplify square root of 3 multiplied by the fifth root of 3.

Let's look into the product law a^m × aⁿ = a^m+n under exponent rule

Answer: Square root of 3 multiplied by the fifth root of 3 is 3^(7⁄₁₀)

Let's put the question in form of expression and solve further

Explanation:

As per the product law,

a^m × aⁿ = a^m+n 

Square root of 3 = 3^1⁄₂

Fifth root of 3 = 3^1⁄5     

Here we have a = 3, m = ¹⁄₂ and n = ¹⁄₅

= 3^1⁄₂ × 3^1⁄₅

= 3^{(1⁄₂+1⁄₅)}

= 3^{(5+2⁄₁₀)}

= 3^(7⁄₁₀)

Hence, the square root of 3 multiplied by the fifth root of 3 is 3^(7⁄₁₀)