3. $$ \frac{(-2 a)^{3} imes\left(3 a^{3} b^{-2} ight)^{2}}{72 a^{4} b^{5}} $$

Question

3. $$ \frac{(-2 a)^{3} 	imes\left(3 a^{3} b^{-2}ight)^{2}}{72 a^{4} b^{5}} $$

UpStudy AI · Accepted Answer

1. Rewrite the expression:
$$
\frac{(-2a)^3 \times \left(3a^3 b^{-2}\right)^2}{72a^4b^5}
$$

2. Simplify $$(-2a)^3$$:
$$
(-2a)^3 = (-2)^3 \times a^3 = -8a^3
$$

3. Simplify $$\left(3a^3 b^{-2}\right)^2$$:
$$
\left(3a^3 b^{-2}\right)^2 = 3^2 \times (a^3)^2 \times \left(b^{-2}\right)^2 = 9a^6b^{-4}
$$

4. Multiply the simplified terms in the numerator:
$$
-8a^3 \times 9a^6b^{-4} = -72a^{3+6}b^{-4} = -72a^9b^{-4}
$$

5. Substitute back into the original expression:
$$
\frac{-72a^9b^{-4}}{72a^4b^5}
$$

6. Cancel the common factor $$72$$:
$$
\frac{-72a^9b^{-4}}{72a^4b^5} = -\frac{a^9b^{-4}}{a^4b^5}
$$

7. Simplify the powers of $$a$$ and $$b$$:

- For $$a$$:
   $$
   \frac{a^9}{a^4} = a^{9-4} = a^5
   $$
   
   - For $$b$$:
   $$
   \frac{b^{-4}}{b^5} = b^{-4-5} = b^{-9}
   $$

8. Write the final simplified expression:
$$
-\frac{a^5}{b^9}
$$
$$ -\frac{a^5}{b^9} $$

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