Final answer:
The expression ((5m^(-4)b^(-7))/(4m^(-9)b^(5)))^(-3) is simplified by converting negative exponents into positive exponents, changing the order of the numerator and denominator. Finally, we get 64m^15*b^36/125.
Step-by-step explanation:
To simplify the given expression ((5m^(-4)b^(-7))/(4m^(-9)b^(5)))^(-3), we first use the property that any term to a negative exponent is equal to one divided by the term to the positive exponent.
So, for example, m^-4 can be rewritten as 1/m^4 and b^-7 as 1/b^7. Similarly, m^-9 is 1/m^9 and b^5 remains the same because its exponent is already positive.
Therefore, ((5m^(-4)b^(-7))/(4m^(-9)b^(5)))^(-3) becomes (5/(4m^5*b^12))^(-3).
Again using the property of negative exponents, 'A' to the power -n equals 1/(A to the power n), we can change the expression to (4m^5*b^12/5)^3.
Resolving the cube, the answer will be 64m^15b^36/125.
Learn more about Simplifying Exponents