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Chapter 2: Problem 50

Simplify the expression using the product rule. Leave your answer in exponential form. $$5^{2} \cdot 5^{3} \cdot 5^{4}$$

Short Answer

Expert verified
The simplified expression using the product rule is \(5^9\).

Step by step solution

01

Apply the product rule for exponents

Since we're given 3 terms of the same base (5) with different exponents (2, 3, and 4), we can apply the product rule, which states: if we multiply two or more powers with the same base, we add their exponents. \[ 5^{2} \cdot 5^{3} \cdot 5^{4} = 5^{(2+3+4)} \]
02

Simplify the expression

We add the exponents 2, 3, and 4, and rewrite the expression with the new exponent. \[ 5^{(2+3+4)} = 5^{(9)} \]
03

Write the answer in exponential form

The expression is already simplified and in exponential form. \[ \boxed{5^9} \] is the simplified expression using the product rule and in exponential form.

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Most popular questions from this chapter

Perform the operation as indicated. Write the final answer without an exponent. \(\frac{-4.5 \times 10^{-6}}{-1.5 \times 10^{-8}}\)

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