Question

Simplify. All variables represent nonnegative numbers.

(a^1/2)^2 sqrt(a^2)

Answer 1

`a^2`

Explanation:

We can refer to the law of exponent where:

`\displaystyle{\left(a^(m)/(n) \right)^k = a^(mk)/(n)}`

Multiply the exponents in. Therefore, we have:

`\displaystyle{a √(a^2) = a√(a \cdot a)}`

Take two a-terms out of the square root and make them one:

`\displaystyle{a √(a^2) = a\cdot a}\\\\\displaystyle{a√(a^2) = a^2}`