Simplify square root of 2 multiplied by the cube root of 2.

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

Answer: Square root of 2 multiplied by the cube root of 2 is equal to 2^(5/6).

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

Explanation:

As per the product law,

a^m × aⁿ = a^m+n 

The square root of 2 = 2^1⁄₂

Cube root of 2 = 2^1⁄₃

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

⇒ 2^1/2 × 2^1/3

⇒ 2^{(1/2 + 1/3)}

⇒ 2^(3+2)/6

⇒ 2^5/6

Hence, the square root of 2 multiplied by the cube root of 2 is 2^5/6.