Final answer:
In mathematics, inverse operations reverse the effect of the original operation. To perform the inverse of addition, subtraction, multiplication, or exponents, use the respective counterparts: subtraction, addition, division, or roots/negative exponents. These principles are evident in scientific notation and fundamental arithmetic operations.
Step-by-step explanation:
The inverse operations for the given operations are as follows: If the operation is add 24, the inverse is subtract 24. When you raise to the 24th power, the inverse is to take the 24th root. If you divide by 24, then you would multiply by 24 for the inverse operation. Similarly, if the operation is subtract 24, the inverse is add 24, and finally, if you multiply by 24, the inverse is to divide by 24. Understanding these operations can be helpful in algebra and can make complex calculations easier to perform.
For example, in scientific notation, we often perform operations on powers of ten. If we have a large number such as 4.5 × 10⁹ (4.5 times 10 to the power of 9), to divide this by another power of ten, we subtract the exponents. This simplifies calculations significantly, as seen in 10⁶ / 10 = 10³ (a million divided by a thousand equals a thousand).
Understanding the relationship between multiplication and division is also crucial. Dividing by 8 is the same as multiplying by its reciprocal, which is 1/8. Similarly, if we want to invert a power of a number, such as 3⁴, we use a negative exponent to represent its reciprocal, resulting in 1/3⁴ or 3⁻⁴.