To simplify \(\left(ab\right)^{-3}\), we need to apply the property of exponents that states:

\[
\left(ab\right)^{-n} = \frac{1}{\left(ab\right)^n}
\]

Applying this to our expression:

\[
\left(ab\right)^{-3} = \frac{1}{\left(ab\right)^3}
\]

Now, use the property \(\left(ab\right)^3 = a^3 b^3\):

\[
\frac{1}{\left(ab\right)^3} = \frac{1}{a^3 b^3}
\]

So, the simplified form is:

\[
\left(ab\right)^{-3} = \frac{1}{a^3 b^3}
\]

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you simplify \(\left(2x\right)^{-4}\)?
2. What is the result of \(\left(xy\right)^{-2} \times \left(xy\right)^5\)?
3. How can you rewrite \(\frac{1}{\left(abc\right)^2}\) using negative exponents?
4. What does \(\left(\frac{a}{b}\right)^{-3}\) simplify to?
5. How would you simplify \(\left(x^2 y\right)^{-1}\)?

**Tip:** Remember, negative exponents indicate the reciprocal of the base raised to the positive exponent.

Learn how to simplify the expression (ab)^{-3} step by step using the laws of exponents. This detailed guide explains the use of exponent rules, converting negative exponents to positive by taking the reciprocal, and applying them to simplify expressions. Suitable for students in Grades 7-9.

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