https://file.aiquickdraw.com/mathbot/file/1728529510362prw7p8gt.jpg

The expression shown in the image is:

\[
w^5 \cdot w^{-7} \cdot w
\]

To simplify this, we apply the laws of exponents. Specifically, the rule:

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

This means we can add the exponents of the same base (in this case, \(w\)).

\[
w^5 \cdot w^{-7} \cdot w^1 = w^{5 + (-7) + 1} = w^{-1}
\]

So the simplified expression is:

\[
w^{-1} = \frac{1}{w}
\]

Would you like more details on how exponent rules were applied or have any other questions?

Here are 5 related questions for practice:
1. How would you simplify \( x^3 \cdot x^{-2} \cdot x^4 \)?
2. What is the result of \( a^5 \cdot a^{-5} \)?
3. Simplify \( y^{-2} \cdot y^3 \cdot y^0 \).
4. How do you simplify an expression like \( z^7 \cdot z^{-3} \)?
5. What is the meaning of a negative exponent?

**Tip**: Always add or subtract the exponents when multiplying terms with the same base.

Learn how to simplify the expression w^5 * w^{-7} * w by applying the laws of exponents. This problem demonstrates the concept of adding exponents when multiplying terms with the same base. Suitable for students in Grades 8-10.

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