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Chapter 0: Problem 12

Evaluate each exponential expression. $$2^{-6}$$

Short Answer

Expert verified
The answer to \(2^{-6}\) is \(\frac{1}{64}\).

Step by step solution

01

Understanding the exponent notation

Remember, an exponent refers to the number of times a number is multiplied by itself. So, \(2^3 = 2 * 2 * 2 = 8\). However, in our case, the exponent is -6. It's important to understand that any nonzero number to the power of -1 is its reciprocal. In general, for any nonzero number \(a\), \(a^{-n} = \frac{1}{a^n}\).
02

Apply the rule of negative exponent

We apply the rule of negative exponents which simply states that \(a^{-n} = \frac{1}{a^n}\). So we write \(2^{-6}\) as \(\frac{1}{2^6}\).
03

Evaluating the expression

Now we calculate the value of \(2^6\) which is \(2 * 2 * 2 * 2 * 2 * 2 = 64\). So, \(\frac{1}{2^6} = \frac{1}{64}\).

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Most popular questions from this chapter

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. The toll to a bridge is \(\$ 3.00 .\) A three-month pass costs \(\$ 7.50\) and reduces the toll to \(\$ 0.50 .\) A six-month pass costs \(\$ 30\) and permits crossing the bridge for no additional fee. How many crossings per three-month period does it take for the three-month pass to be the best deal?

Will help you prepare for the material covered in the first section of the next chapter. If \(y=|x+1|,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -4 and ending with 2

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Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost \(\$ 175 .\) The mechanic charges \(\$ 34\) per hour. If you receive an estimate for at least \(\$ 226\) and at most \(\$ 294\) for fixing the car. what is the time interval that the mechanic will be working on the job?

Explain how to add or subtract rational expressions with the same denominators.
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