Simplify

Problem

√(,√(,b))/√(3,a*b)

Solution

1. Convert radicals to fractional exponents using the rule √(n,x)=x(1/n)

√(,√(,b))=(b(1/2))(1/2)

√(3,a*b)=(a*b)(1/3)

2. Apply the power of a power rule (xm)n=x(m⋅n) to the numerator.

(b(1/2))(1/2)=b(1/4)

3. Apply the power of a product rule (x*y)n=xn*yn to the denominator.

(a*b)(1/3)=a(1/3)*b(1/3)

4. Combine the terms into a single fraction.

(b(1/4))/(a(1/3)*b(1/3))

5. Apply the quotient rule (bm)/(bn)=b(m−n) to the variable b

b(1/4−1/3)=b(3/12−4/12)

b(−1/12)

6. Rewrite with positive exponents using the rule x(−n)=1/(xn)

1/(a(1/3)*b(1/12))

Final Answer

√(,√(,b))/√(3,a*b)=1/(a(1/3)*b(1/12))

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