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Chapter 5: Problem 147

How do you know if an exponential expression is simplified?

Short Answer

Expert verified
An exponential expression is considered simplified if there are no simple factors left to combine, no like terms that can be combined, and any fractions are in their simplest form.

Step by step solution

01

Check for simple factors

The first step in any simplification is to check for simple numerical factors which can be simplified. If there are none, the expression is likely simplified. For example, in the expression \(2^{4} \cdot 2^{3}\), we can consolidate the powers to get \(2^{7}\), which is simplified.
02

Check for like terms

Next, look for any 'like terms' that need to be combined. In terms of exponents, 'like terms' would refer to terms with the same base and exponent. If no like terms are present, the expression can be considered simplified. For example, in \(7^{5} + 7^{5}\), we can combine these like terms to get \(2 \cdot 7^{5}\).
03

Check for simplified fractions

Finally, if the exponential expression has fractions, check that the fraction is in its simplest form. This means that the numerator and the denominator have no common factors. If the fraction is already in its simplest form, then the expression is simplified. For example, \((2^{6}/2^{2})\), can be simplified to \(2^{4}\) according to the laws of exponents.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$(y-1)\left(y^{2}+y+1\right)=y^{3}-1$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I used the product rule for exponents to multiply \(x^{7}\) and \(y^{9}\)

Express \(\frac{7}{8}\) as a decimal. (Section \(1.3,\) Example 4 )

Perform the indicated operations. $$(y+5)^{2}-(y-4)^{2}$$

Perform the indicated computations. Express answers in scientific notation. $$\left(5 \times 10^{3}\right)\left(1.2 \times 10^{-4}\right) \div\left(2.4 \times 10^{2}\right)$$
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