What is 3 to the -4 times 3 to the -8 times 3 to the -14?

To solve \(3^{-4} \times 3^{-8} \times 3^{-14}\), we can use the rule of exponents that states:

\[
a^m \times a^n = a^{m+n}
\]

Applying this rule, we combine the exponents by adding them:

\[
3^{-4} \times 3^{-8} \times 3^{-14} = 3^{(-4) + (-8) + (-14)}
\]

Now, calculate the sum of the exponents:

\[
-4 + (-8) + (-14) = -4 - 8 - 14 = -26
\]

So, we have:

\[
3^{-4} \times 3^{-8} \times 3^{-14} = 3^{-26}
\]

Thus, the answer is:

\[
3^{-26}
\]

Let me know if you'd like further clarification on any part of this process!

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Here are some related questions for practice:

1. What is \(2^{-3} \times 2^{-7} \times 2^{-2}\)?
2. How would you simplify \(5^{-2} \times 5^3\)?
3. What is the value of \(7^{-5} \times 7^{-10}\)?
4. If you have \(10^{-6} \times 10^2\), what is the result?
5. What does \(4^{-1} \times 4^{-1} \times 4^{-1}\) simplify to?

**Tip:** When multiplying powers of the same base, always add the exponents together.

Discover how to simplify the expression 3^-4 × 3^-8 × 3^-14 using the rules of exponents. This explanation includes a step-by-step breakdown of combining exponents and is suitable for students in Grades 6-8.

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