Simplify fourth root of b^5 square root of b

Problem

√(4,b5√(,b))

Solution

1. Convert the radicals into fractional exponents using the rule √(n,xm)=bm/n

√(4,b5⋅b1/2)

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

b5⋅b1/2=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.

(b11/2)1/4

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

11/2⋅1/4=11/8

Final Answer

√(4,b5√(,b))=b11/8

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