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Chapter 0: Problem 22

Evaluate each exponential expression. $$\frac{3^{4}}{3^{7}}$$

Short Answer

Expert verified
The evaluation of \(\frac{3^{4}}{3^{7}}\) gives \(\frac{1}{27}\).

Step by step solution

01

Understand the Problem

We are given two exponential terms \(3^{4}\) and \(3^{7}\) with the same base 3. We have to divide \(3^{4}\) by \(3^{7}\).
02

Apply Laws of Exponents

When dividing terms with the same base, we subtract the exponents. Therefore, we rewrite the problem as \(3^{4-7}\).
03

Evaluate the Expression

Subtracting the exponents gives \(3^{-3}\). This could also be written as \(\frac{1}{3^{3}}\).
04

Solve \(\frac{1}{3^{3}}\)

Finally, once we solve \(\frac{1}{3^{3}}\), we get \(\frac{1}{27}\) as the result.

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Most popular questions from this chapter

$$\text { factor completely.}$$ $$x^{4}-y^{4}-2 x^{3} y+2 x y^{3}$$

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$

Evaluate each algebraic expression for the given value or values of the variable(s). $$8+6 x, \text { for } x=5$$

Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)

Rewrite each expression without absolute value bars. $$|300|$$
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