Simplify the following expression to simplest form using only positive exponents
(64x^3 y^9) ^-2/3
To simplify the expression (64x^3 y^9) ^-2/3, we need to apply the negative exponent to both the base and the exponent of the expression.
The negative exponent can be written as the reciprocal of the positive exponent. So, we have:
(1/ (64x^3 y^9) ^2/3)
To simplify further, we can raise both the numerator and the denominator to the power of 3:
(1^3 / (64x^3 y^9)^2)
This gives:
1 / (64^2 x^6 y^18)
Simplifying further:
1 / (4096 x^6 y^18)
Therefore, the simplest form of the expression (64x^3 y^9)^-2/3 is 1 / (4096 x^6 y^18).