Write the expression equivalent to ((q^4)^-3)/(q^-15)
To simplify the expression ((q^4)^-3)/(q^-15), we can apply the properties of exponentiation.
First, let's simplify the numerator. According to the power of a power rule, when we raise a power to another power, we multiply the exponents. So, (q^4)^-3 can be rewritten as q^(4*-3) which is equal to q^-12.
Next, let's simplify the denominator. According to the negative exponent rule, q^-15 can be rewritten as 1/q^15.
Now, our expression becomes q^-12 / (1/q^15).
To divide by a fraction, we can multiply by its reciprocal. So, we multiply q^-12 by q^15/1.
Therefore, the expression is simplified to q^-12 * (q^15/1).
Using the product of powers rule, we can add the exponents when multiplying powers with the same base. Therefore, q^-12 * q^15 can be simplified as q^(-12+15) = q^3.
Thus, the expression ((q^4)^-3)/(q^-15) is equivalent to q^3.