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

2 Answers
Jun 22, 2018

= ((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)

Jun 23, 2018

=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)