Multiply: a−^4(a^2)(a−^5)
A. 1/a^6
B. a^40
C. a^7
D. 1/a^7

Let's multiply the expression \( a^{-4} \cdot a^2 \cdot a^{-5} \).

We use the rule of exponents that states when multiplying powers with the same base, you add the exponents:

\[
a^{-4} \cdot a^2 \cdot a^{-5} = a^{-4 + 2 - 5}
\]

Now, calculate the exponent:

\[
-4 + 2 - 5 = -7
\]

So, the expression simplifies to:

\[
a^{-7}
\]

This can also be written as:

\[
\frac{1}{a^7}
\]

The correct answer is:

**D. \(\frac{1}{a^7}\)**

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. What is the value of \(a^{-3} \cdot a^5\)?
2. How do you simplify \(a^2 \cdot a^{-2}\)?
3. What happens when you divide two exponents with the same base?
4. What is the result of \(a^4 \cdot a^{-1}\)?
5. How do you express \(a^{-1}\) as a fraction?

**Tip:** Negative exponents indicate a reciprocal, so \(a^{-n}\) equals \(\frac{1}{a^n}\).

Learn how to simplify the exponential expression a^-4 * a^2 * a^-5 step-by-step. This problem involves using the rules of exponents to combine powers with the same base. Suitable for Grades 7-9.

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