Graduate Management Admission Test (GMAT) Practice Test

What does the expression ᵇ√(nᵃ) simplify to?

1. ᵇ√n * nᵃ

2. (ᵇ√n)ᵃ

3. nᵃ/ᵇ

4. (nᵃ)ᵇ

The correct answer is: (ᵇ√n)ᵃ

The expression ᵇ√(nᵃ) represents the b-th root of n raised to the power of a. To simplify this expression, we can utilize the property of exponents that states that taking the b-th root of a number is equivalent to raising that number to the power of 1/b. Thus, we can rewrite the expression as follows: ᵇ√(nᵃ) = (nᵃ)^(1/b) When applying the power of a power rule in exponents, which asserts that (x^m)^n = x^(m*n), we can multiply the exponents: (nᵃ)^(1/b) = n^(a*(1/b)) = n^(a/b). However, the crucial aspect of the original expression is often misinterpreted. Instead of separating into further components, we can recognize that this expression retains its structure in terms of manipulation with roots: Also, utilizing the property of exponents, we see that taking the b-th root of n raised to a power can be expressed as raising the base n to the fraction of its exponent divided by b. Thus, after simplification, the clean form of this expression results in (ᵇ