Final answer:
This illustrates the division property of equality and touches on the concept of negative exponents in algebra.
Step-by-step explanation:
The equation 3x = -21 is an example of an algebraic equation that can be solved using the division property of equality. To isolate the variable x, you need to perform the same operation on both sides of the equation. Therefore, to solve for x, you divide both sides by 3, getting the result x = -7.
In terms of exponents, the example you mentioned about inversion or dividing by x, highlights the concept of negative exponents. When you have a negative exponent, such as x-1, this implies 1/x. Following the rule of adding exponents, if we have 34 * 3-4 we get 34-4 which is 30. Since any number raised to the zero power equals 1 (anything to the power of zero is one), 3-4 is equivalent to 1/34 or in expanded form 1/(3*3*3*3).