Final answer:
The correct expression equivalent to (q^4)^-3 / q^-15 is q^3, which is not listed among the provided answer choices. The correct option is D.
Step-by-step explanation:
To simplify the expression (q4)-3/q-15, we can apply the rule of exponents: when dividing exponential terms with the same base, subtract the exponents. In this case, (q4)-3/q-15 can be rewritten as q4-(-15) which is equivalent to q4+15.
Adding the exponents gives us q19. Therefore, the expression (q4)-3/q-15 is equivalent to q19.
So, the correct option is d) q19.
The question asks which expression is equivalent to the mathematical expression (q4)-3 / q−15. To simplify this expression, we use the properties of exponents. If we have an expression of the form (ab)c, this is equivalent to ab × c. That means (q4)-3 can be simplified to q4 × (-3) or q−12. Now we have to divide this by q−15, which according to the quotient rule of exponents (an / am = an − m) gives us q(−12) − (−15) or q− 12 + 15 which simplifies to q3. Therefore, none of the answer choices (a) q−12, (b) q12, (c) q−7, (d) q7 are correct, and the correct answer is q3.
To simplify the expression (q4)-3/q-15, we can apply the rule of exponents: when dividing exponential terms with the same base, subtract the exponents. In this case, (q4)-3/q-15 can be rewritten as q4-(-15) which is equivalent to q4+15.
Adding the exponents gives us q19. Therefore, the expression (q4)-3/q-15 is equivalent to q19.
So, the correct option is d) q19.