\sqrt{b^(6)} What is the rational exponent form of this expression?

Question

`\sqrt{b^(6)}` What is the rational exponent form of this expression?

Answer 1

If you choose to fully simplify this expression, then the answer is b^3

If you just want to convert to rational exponent form, then the square root will be replaced with an exponent of 1/2. The rule is sqrt(x) = x^(1/2)

So,

sqrt(b^6) = (b^6)^(1/2)

which can be written as

`√(b^6) = \left(b^6\right)^(1/2)`

note how the exponents 6 and 1/2 multiply to 3, which is why the fully simplified version is b^3