Simplify. Write the answer using positive exponents only. (x^-5y^-6/a^-5)^-3
(x^15 y^18)/a^15
To simplify (x^-5y^-6/a^-5)^-3 and write the answer using positive exponents only, we can follow these steps:
Step 1: Apply the power rule of exponents. When a base with a negative exponent is raised to a negative power, it becomes positive.
In this case, (x^-5y^-6/a^-5)^-3 becomes (1/x^5y^6 * a^5)^3.
Step 2: Simplify within the parentheses.
Multiplying the exponents inside the parentheses gives us (1/x^5y^6 * a^5)^3 = (1/x^5y^6 * a^15).
Step 3: Apply the power rule of exponents again to the entire expression.
Raising a product to a power is the same as raising each factor to that power, so (1/x^5y^6 * a^15)^3 becomes 1^3 / (x^5y^6)^3 * (a^15)^3.
Step 4: Simplify further.
The expression becomes 1 / (x^15y^18 * a^45).
Therefore, the simplified form of (x^-5y^-6/a^-5)^-3 using positive exponents only is 1 / (x^15y^18 * a^45).