To simplify the expression \(4^{10} - 4^9\), we can factor out the common term \(4^9\):

\[
4^{10} - 4^9 = 4^9 \cdot (4 - 1)
\]

Since \(4 = 4^1\), we have:

\[
4^9 \cdot (4 - 1) = 4^9 \cdot 3
\]

Now, we know that \(4^9 = (2^2)^9 = 2^{18}\), so:

\[
4^{10} - 4^9 = 3 \cdot 4^9 = 3 \cdot 2^{18}
\]

Therefore, the simplified form of \(4^{10} - 4^9\) is:

\[
3 \cdot 4^9 \text{ or } 3 \cdot 2^{18}
\]

If you want the numerical value:

\[
4^{10} = 1,048,576 \quad \text{and} \quad 4^9 = 262,144
\]

Thus:

\[
4^{10} - 4^9 = 1,048,576 - 262,144 = 786,432
\]

So, the expression simplifies to \(786,432\).

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Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor out terms in expressions involving exponents?
2. What are the properties of exponents, such as \(a^m \cdot a^n = a^{m+n}\)?
3. How can expressions involving powers of 2 be simplified?
4. What are some methods to compute large exponents quickly?
5. How can we use logarithms to solve exponential equations?

**Tip:** Factoring common terms is a powerful tool for simplifying algebraic expressions.

Learn how to simplify the expression 4^10 - 4^9 by factoring out common terms and applying properties of exponents. This problem covers essential algebraic concepts suitable for Grades 8-10, providing a step-by-step explanation and numerical calculations.

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