Simplify (m^(1/4)n^(1/2))^2(m^2n^3)^(1/2)

Problem

(m(1/4)*n(1/2))2*(m2*n3)(1/2)

Solution

1. Apply the power of a product rule to the first part of the expression by multiplying the outer exponent 2 by each inner exponent.

(m(1/4⋅2))*(n(1/2⋅2))

m(1/2)*n1

2. Apply the power of a product rule to the second part of the expression by multiplying the outer exponent 1/2 by each inner exponent.

(m(2⋅1/2))*(n(3⋅1/2))

m1*n(3/2)

3. Combine the results by multiplying the simplified parts together.

(m(1/2)*n)*(m*n(3/2))

4. Apply the product rule for exponents by adding the exponents of the terms with the same base.

m(1/2+1)*n(1+3/2)

5. Simplify the exponents by finding a common denominator for the fractions.

m(3/2)*n(5/2)

Final Answer

(m(1/4)*n(1/2))2*(m2*n3)(1/2)=m(3/2)*n(5/2)

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