Simplified equation - 3*x^10.6666666666667* y^6/40
Sure, let's break down the process in steps.
1. First let's re-write the expression for clarity:
(6x^(2/3)y/5) ÷ [(4x^-5)^2 / y^5]
2. Next, simplify the expressions inside the brackets:
(6x^(2/3)y/5) ÷ [16x^-10 / y^5]
3. Now, in general dividing by a fraction is the same as multiplying by its reciprocal (flipping the nominator and denominator). So, we reverse the fraction in the divisor:
(6x^(2/3)y/5) * (y^5/16x^-10)
4. Now, multiplications can be rearranged, so let's group like elements together:
(6/5*1/16) * (x^(2/3)/x^-10) * y * y^5
5. Simplify the constant term at front:
(3/40) * (x^(2/3) * x^10) * y^6
6. Now, to multiply exponents with the same base (x here), we add the powers.
(Keep in mind that x^(2/3)=x^(20/30) and x^10=x^(300/30) and -x^10=-x^(300/30).)
This yields: (3/40) * x^(20/30+300/30) * y^6
7. Adding the powers gives (3/40) * x^(320/30) * y^6 or
8. Simplifying further gives: 3*x^10.6666666666667 * y^6 /40
So, the simplified expression with positive powers is 3*x^10.6666666666667* y^6/40.