Simplify the following expression to simplest form using only positive exponents
(32x^-30y^15)^3/5
To simplify the expression (32x^-30y^15)^3/5 using only positive exponents, we can apply the exponent rule that states (a^m)^n = a^(m*n).
Using this rule, we can simplify the expression as follows:
(32x^-30y^15)^3/5
= 32^(3/5) * x^(-30*3/5) * y^(15*3/5)
Now we simplify each term separately:
32^(3/5)
= (2^5)^(3/5)
= 2^(5*(3/5))
= 2^3
= 8
x^(-30*3/5)
= x^(-90/5)
= x^(-18)
y^(15*3/5)
= y^(45/5)
= y^9
Therefore, the simplified expression is:
8x^-18y^9