Power Rules Assessment Test

When there are two or more exponents and only one base, you multiply the exponents. This means that you raise the base to the power of the sum of the exponents.

The derivative of a constant is always zero because a constant does not change with respect to any variable. Since the derivative represents the rate of change of a function, and a constant has no change, its derivative is always zero.

When a number is raised to the power of zero, the result is always 1. This is because any number raised to the power of zero is equivalent to multiplying that number by itself zero times, which results in the value of 1. Therefore, anything raised to the power of zero is 1.

The given statement, "The derivative of the sum/difference of functions is the sum/difference of the derivatives," aligns with the sum/difference rule of differentiation. This rule states that the derivative of the sum or difference of two functions is equal to the sum or difference of their individual derivatives. Therefore, the correct answer is the sum/difference rule.

When multiplying two powers that have the same base, you add the exponents. This is because the exponent represents the number of times the base is multiplied by itself. So, when you multiply two powers with the same base, you are essentially multiplying the base by itself multiple times. To find the total exponent, you add the exponents together.

When dividing identical bases, you multiply the exponents. This is because when you divide two numbers with the same base, the result is the base raised to the difference of the exponents. For example, if you have x^a / x^b, where x is the base, you can rewrite it as x^(a-b). Therefore, to divide identical bases, you need to subtract the exponents, which is equivalent to multiplying the exponents when they have the same base.

The quotient rule is used to find the derivative of a function that is the ratio of two differentiable functions. It states that the derivative of the quotient of two functions is equal to the numerator's derivative times the denominator minus the denominator's derivative times the numerator, all divided by the square of the denominator. This rule is essential in calculus when dealing with functions that involve division, allowing us to find the rate of change of such functions.

When dividing identical bases, you subtract the exponents. This is because when you divide two numbers with the same base, the result is equal to the base raised to the difference of the exponents. Therefore, subtracting the exponents gives you the correct result.

The exponent rule refers to a functional relationship between two quantities where a relative change in one quantity leads to a proportional relative change in the other quantity. This means that the relationship between the two quantities can be expressed using an exponent, where the change in one quantity is raised to a certain power to determine the change in the other quantity. The exponent rule helps to quantify the proportional relationship between the two quantities.

A character that is set slightly above the normal line of type is referred to as a superscript. Superscripts are commonly used in mathematical equations, scientific notations, and footnotes to indicate exponents, references, or smaller characters. By positioning the character higher than the baseline, it appears smaller and slightly elevated, making it easier to distinguish from the rest of the text.