Simplify the expression below to find the values of $$ x, y $$ and $$ z $$. $$ \frac{\left(a^{-3} b^{4} ight)^{-5}}{(a b)^{3} c^{-6}} imes \frac{a}{b^{-3} c^{2}}=a^{x} b^{y} c^{z} $$

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Simplify the expression below to find the values of $$ x, y $$ and $$ z $$. $$ \frac{\left(a^{-3} b^{4}ight)^{-5}}{(a b)^{3} c^{-6}} 	imes \frac{a}{b^{-3} c^{2}}=a^{x} b^{y} c^{z} $$

UpStudy AI · Accepted Answer

1. Compute the exponent of the first term:
   $$
   \left(a^{-3} b^{4}\right)^{-5} = a^{-3 \times (-5)} b^{4 \times (-5)} = a^{15} b^{-20}.
   $$

2. Simplify the denominator in the first fraction:
   $$
   (a b)^{3} c^{-6} = a^{3} b^{3} c^{-6}.
   $$

3. Divide the results from steps 1 and 2:
   $$
   \frac{a^{15} b^{-20}}{a^{3} b^{3} c^{-6}} = a^{15-3} b^{-20-3} c^{0-(-6)} = a^{12} b^{-23} c^{6}.
   $$

4. Simplify the second fraction by rewriting the negative exponent:
   $$
   \frac{a}{b^{-3} c^{2}} = a \times b^{3} c^{-2}.
   $$

5. Multiply the results from steps 3 and 4:
   $$
   a^{12} b^{-23} c^{6} \times a \, b^{3} c^{-2} = a^{12+1} b^{-23+3} c^{6-2} = a^{13} b^{-20} c^{4}.
   $$

Comparing with $$ a^{x} b^{y} c^{z} $$, we have:
$$
x = 13,\quad y = -20,\quad z = 4.
$$
$$ x = 13 $$, $$ y = -20 $$, $$ z = 4 $$.

Simplify the expression below to find the values of and .

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