Simplify fourth root of b^5 square root of b

Problem

√(4,b^5√(,b))

Solution

1. Convert the radicals into fractional exponents using the rule √(n,x^m)=b^m/n

√(4,b^5⋅b^1/2)

2. Combine the terms inside the fourth root by adding the exponents, since b^m⋅b^n=b^(m+n)

b^5⋅b^1/2=b^(5+1/2)

3. Simplify the sum in the exponent by finding a common denominator.

5+1/2=10/2+1/2=11/2

4. Apply the outer radical as a fractional exponent to the simplified inner expression.

(b^11/2)^1/4

5. Multiply the exponents using the power of a power rule (b^m)^n=b^(m⋅n)

11/2⋅1/4=11/8

Final Answer

√(4,b^5√(,b))=b^11/8

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