Question

How to solve (49x^2)^3/2 ÷ (9y^4)^3/2?

Answer 1

`= ((7x)/ (3y^2))^3 = (343x^3)/ (27y^6)`

Explanation:

Considering the question to be:

`(49x^2)^(3/2) ÷ (9y^4)^(3/2)`

Solution:
`(49x^2)^(3/2) ÷ (9y^4)^(3/2)` can be written as:

`=>(7^2 x^2)(3/2) ÷ (3^2y^4)^(3/2)`

`=> ((7x)^2)3/2 ÷( (3y^2)^2)^(3/2)`

`=>(7x)^(2xx3/2 )÷ ( 3y^2)^(2xx^3/2)`

`=>(7x)^3÷ ( 3y^2)^3 = ((7x)/ (3y^2))^3`

`=> (343x^3)/ (27y^6)`

Answer 2

`=343/(27x^3)`

Explanation:

`(49x^2)^(3/2)\div(9y^4)^(3/2)`

Fractional exponent: the denominator is the value of the root, and the numerator is an exponent of the value (it goes inside the root).
So `a^(3/2)` becomes `\sqrt(a^3)`

Thus, you now have
`\sqrt((49x^2)^3)\div\sqrt((9y^4)^3)`

Exponent of exponent: multiply them.
`\therefore\sqrt(117649x^6)\div\sqrt(729x^12)`

Change back to fractional exponents for the variable, so you can multiply:
`[\sqrt(117649)\cdot(x^6)^(1/2)]\div[\sqrt(729)\cdot(y^12)^(1/2)]`
`[\sqrt(117649)\cdot(x^3)]\div[\sqrt(729)\cdot(y^6)]`

Now simplify.
`[\sqrt(117649)\cdot(x^3)]/[\sqrt(729)\cdot(y^6)]=(343x^3)/(27y^6)`

(by the way, use a calculator for the square roots)