https://file.aiquickdraw.com/mathbot/file/1723764739497i1ntp93h.jpg

Let's solve the given expression:

The expression is:

\[
(4 - x)^7 \left((4 - x)^6\right)^{-2}
\]

We can simplify this by using the properties of exponents. Specifically, we use the rule:

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

In this case, \(a = (4 - x)\), \(m = 7\), and \(n = -2 \times 6 = -12\).

So the expression simplifies as follows:

\[
(4 - x)^7 \cdot (4 - x)^{-12} = (4 - x)^{7 + (-12)} = (4 - x)^{-5}
\]

So, the equivalent form of the given expression is:

\[
(4 - x)^{-5}
\]

Would you like more details or have any other questions? Here are 8 related questions you might find interesting:

1. How would you express \((4 - x)^{-5}\) in fractional form?
2. What happens if \(x = 4\) in this expression?
3. Can you expand the expression \( (4-x)^7 \)?
4. How does the expression change if the exponent in the original problem was positive instead of negative?
5. What are the properties of exponents used in simplifying this expression?
6. Can this expression be represented as a series expansion?
7. How does this expression behave as \(x\) approaches infinity?
8. What is the domain of the simplified expression?

**Tip:** When dealing with exponents, always remember to carefully apply the rules for combining them to simplify expressions.

Learn how to simplify the expression (4 - x)^7 * ((4 - x)^6)^(-2) using exponent rules. Understand the properties of exponents and how they apply to this problem. Suitable for high school students studying algebra and exponentiation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation