Problem 1 True or False: Raising a positiv... [FREE SOLUTION]

Chapter 2: Problem 1

True or False: Raising a positive base to a negative exponent will give a negative result. (Example: \(2^{-4}\) )

Short Answer

Expert verified

False. Raising a positive base to a negative exponent will not give a negative result, as it is equivalent to the fraction 1 divided by that base raised to the positive exponent, which gives a positive result (Example: \(2^{-4} = \frac{1}{2^4} = \frac{1}{16}\)).

Step by step solution

Review the properties of negative exponents

A negative exponent is the reciprocal of the positive exponent. In other words, if you have a number a raised to the power of -n (a^{-n}), it is equivalent to the fraction 1 divided by that number raised to the power of n (1 / a^{n}).

Apply the properties to the given example

To evaluate if raising a positive base to a negative exponent will give a negative result, let's use the given example: \(2^{-4}\). According to the properties of negative exponents, this can be rewritten as \(\frac{1}{2^4}\).

Evaluate the expression

Calculate the value of \(2^4\), which is 2 * 2 * 2 * 2 = 16. Now, we have the expression \(\frac{1}{16}\).

Determine if the result is positive or negative

Since the base (2) and the exponent (4) are both positive numbers, the result of the expression \(\frac{1}{16}\) is also a positive number. It shows that raising a positive base to a negative exponent does not give a negative result.

Provide the answer

Based on the evaluation, the statement is False. Raising a positive base to a negative exponent will NOT give a negative result.

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91影视

True or False: Raising a positive base to a negative exponent will give a negative result. (Example: \(2^{-4}\) )

Short Answer

Step by step solution

Review the properties of negative exponents

Apply the properties to the given example

Evaluate the expression

Determine if the result is positive or negative

Provide the answer

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