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Chapter 0: Problem 18

Evaluate each exponential expression. $$\frac{3^{8}}{3^{4}}$$

Short Answer

Expert verified
The solution to the given exponential expression \(\frac{3^{8}}{3^{4}}\) is 81.

Step by step solution

01

Identify the Base and Exponents

Here, base=3 and there are two exponents: 8 and 4. The given expression is \(3^{8}/3^{4}\).
02

Apply the Quotient Rule of Exponents

When dividing expressions with the same base, subtract the exponent in the denominator from the exponent in the numerator. By quotient rule, \(3^{8}/3^{4}\) simplifies to \(3^{8-4}\).
03

Simplify the Expression

Subtract the exponents: \(3^{8-4}\) becomes \(3^{4}\).
04

Evaluate the Exponential Expression

The expression \(3^{4}\) equals 81. So, the final solution is 81.

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