Question

Which property of exponents must be used first to solve this expression? (iy2)1/3

Answer 1

Explanation:

"must be used first" is a very hard phrasing. multiplication is commutative.

and I am not sure that the problem is stated correctly.

I read here

(i×y²) to the power of 1/3.

i is the imaginary constant sqrt(-1) ?

exponents brought themselves to the power of something else multiply.

e.g.

`({2}^(3))^(4) = {2}^(12)`

exponents in multimedia expressions of the same base simply add up.

e.g.

`{2}^(3) * {2}^(4) = {2}^(7)`

a negative exponent means that the expression with the same positive exponent is just at the bottom of a division.

e.g.

`{2}^( - 3) = 1 / {2}^(3)`

and a fraction as exponent specifies a root to be taken.

e.g

`{2}^(1 / 3) = \sqrt[3]{2}`

so, I would do all the exponent multiplications to simplify the expression.

`\sqrt[3]{i * {y}^(2) } = ({i * {y}^(2) })^(1 / 3) =`

`= ( { - 1}^(1 / 2) * {y}^(2) ) ^(1 / 3)`

1/2 × 1/3 = 1/6

2 × 1/3 = 2/3

`= { - 1}^(1 / 6) * {y}^(2 / 3) = \sqrt[6]{ - 1} * \sqrt[3]{ {y}^(2) }`

so, as we can see, we can move freely from multiplying the fraction exponents to converting them into root expressions and vice versa.