Final answer:
The multiplicative inverse of 1/4 is 4, as multiplying them gives 1. For the algebraic expression 5t-1/4, each term's inverse is taken separately to get 1/(5t) - 4 as the multiplicative inverse. This concept is foundational in algebra and helps with understanding operations involving fractions and exponents.
Step-by-step explanation:
Understanding Multiplicative Inverses
The multiplicative inverse of a number is another number which, when multiplied together, yields the product 1. For any non-zero number a, the multiplicative inverse is 1/a. Applying this definition, the multiplicative inverse of 1/4 is simply 4, because 1/4 × 4 = 1. Now, looking at the algebraic expression 5t-1/4, its multiplicative inverse would be the reciprocated form where both terms in the expression are inverted. Consequently, the multiplicative inverse of 5t-1/4 is 1/(5t) - 4.
Illustrating this with an example: if we have a number like 2.5, following the idea that we should 'forget where the decimal point is,' we identify the essential feature of the number and flip it, yielding a multiplicative inverse that starts with 4, e.g., 2.5's multiplicative inverse is 0.4.
In the context of exponents and inverses, for example, a⁻¹ = 1/a. And if we consider a to be 1/4 in this case, raising it to the negative one power gives us (1/4)⁻¹ which is 4, confirming our previous result for the multiplicative inverse.