Question

Which expression is equivalent to (m−2n−3)−3?

a) m⁶n⁹
b) m^−6n^−9
c) m^−5n^−6
d) 1 / (m⁵n⁶)

Answer 1

The equivalent expression for (m−2n−3)−3 is 1 / (m⁵n⁶), using the negative exponent rule which states that a term with a negative exponent is equivalent to the reciprocal of that term with a positive exponent.

Step-by-step explanation:

The expression (m−2n−3) taken to the power of −3 implies that each part of the expression inside the parentheses is raised to the power of −3. This process is known as negative exponentiation. The rules of exponents state that a term with a negative exponent is equivalent to the reciprocal of that term with a positive exponent.

Applying this, the expression becomes m raised to the −3, 2n raised to the −3, and 3 raised to the −3, which simplifies to m⁻³, (2n)⁻³, and 3⁻³. When you cube 2 and 3, you get 8 and 27 respectively, thus the expression simplifies further.

So, the equivalent expression is 1 / (m⁵n⁶), as this represents the reciprocal of each term with its respective exponent turned positive.

Therefore, the correct answer is: d) 1 / (m⁵n⁶).