Simplify the expression $$\frac{a^{7} imes b^{8} imes c^{7}}{a^{9} imes b^{5} imes c^{4}}$$.

Question

Simplify the expression $$\frac{a^{7} 	imes b^{8} 	imes c^{7}}{a^{9} 	imes b^{5} 	imes c^{4}}$$.

Accepted Answer

**Solution:**

1. Given expression:
   $$\frac{a^{7} 	imes b^{8} 	imes c^{7}}{a^{9} 	imes b^{5} 	imes c^{4}}$$

2. Apply the laws of exponents: $$\frac{x^{m}}{x^{n}} = x^{m-n}$$ for each variable separately.

3. Simplify each variable:
   - For *a*: $$a^{7} \div a^{9} = a^{7-9} = a^{-2}$$
   - For *b*: $$b^{8} \div b^{5} = b^{8-5} = b^{3}$$
   - For *c*: $$c^{7} \div c^{4} = c^{7-4} = c^{3}$$

4. Combine the simplified terms:
   $$a^{-2} 	imes b^{3} 	imes c^{3}$$

**Answer:** $$(a^{-2}) 	imes (b^{3}) 	imes (c^{3})$$

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