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Chapter 0: Problem 21

Evaluate each exponential expression. $$\frac{2^{3}}{2^{7}}$$

Short Answer

Expert verified
The simplified form of \(\frac{2^{3}}{2^{7}}\) is \(\frac{1}{2^{4}}\)

Step by step solution

01

Writing the expression

The given expression is \(\frac{2^{3}}{2^{7}}\)
02

Applying the properties of exponents

When dividing expressions with same base, subtract the exponent of the denominator from the exponent of the numerator. The equation becomes \(2^{3-7}\)
03

Solving the mathematical expression

Subtract the exponents, which gives \(2^{-4}\). In maths, when an exponent is negative, it means the base is on the wrong side of the fraction line, so flip the base to the other side. The final simplified result is \(\frac{1}{2^{4}}\)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

Give an example of a number that is a rational number, an integer, and a real number.

Simplify and express the answer in descending powers of \(x\) : $$2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right)$$

Factor and simplify each algebraic expression. $$-8(4 x+3)^{-2}+10(5 x+1)(4 x+3)^{-1}$$

Give an example of a rational number that is not an integer.
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