https://file.aiquickdraw.com/mathbot/file/1728316670828ep8cnjr8.jpg

The equation shown in the image is:

\[
4^m \cdot 4^4 = 4^{-5}
\]

We can use the property of exponents that states:

\[
a^x \cdot a^y = a^{x + y}
\]

Applying this property to the left side of the equation:

\[
4^m \cdot 4^4 = 4^{m+4}
\]

Now, we can rewrite the equation as:

\[
4^{m+4} = 4^{-5}
\]

Since the bases are the same (both are powers of 4), we can set the exponents equal to each other:

\[
m + 4 = -5
\]

Now, solve for \( m \):

\[
m = -5 - 4 = -9
\]

Thus, the value of \( m \) is:

\[
\boxed{-9}
\]

Do you want more details or have any questions?

Here are 5 related questions:
1. What is the general rule for multiplying powers with the same base?
2. How would you solve \( 3^x \cdot 3^2 = 3^5 \) for \( x \)?
3. What happens if the exponents are negative in a multiplication problem?
4. How can you simplify \( 2^3 \cdot 2^x = 2^8 \)?
5. Can you explain how to solve \( 5^x \cdot 5^{-1} = 5^4 \)?

**Tip**: When solving equations with exponents, always try to express both sides with the same base so you can compare the exponents easily.

What is the value of m in the equation 4^m * 4^4 = 4^(-5)?

Learn how to solve the exponent equation 4^m * 4^4 = 4^(-5) using the properties of exponents. This step-by-step solution involves applying the rule for multiplying powers with the same base. Suitable for students in Grades 8-10.

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