Question

1)(с-8 степень) - 9 степень ---------------------- с - ⁴ 2)(с-5 степень) - ⁴ --------------------------- с-²

Answer 1

$\frac{(c^{-8})^{-9}}{c^{-4}} = \frac{c^{72}}{c^{-4}} = c^{72-(-4)}= c^{76}$

$\frac{(c^{-5})^{-4}}{c^{-2}}= \frac{c^{20}}{c^{-2}} = c^{20-(-2)}= c^{22}$

Answer 2

To simplify the expressions, let's handle each of them step by step:

1. $\frac{(c^8 - c^9)}{(c^4)}$

Step 1: Factor out $c^8$ from the numerator: $c^8(1 - c)$

Step 2: Rewrite the expression: $\frac{c^8(1 - c)}{c^4}$

Step 3: Cancel out common factors from the numerator and denominator: $\frac{(1 - c)}{c^{4-8}} = \frac{(1 - c)}{c^{-4}}$

Step 4: Negative exponent means taking the reciprocal: $\frac{(1 - c)}{1/c^4} = (1 - c) \cdot c^4 = c^4 - c^5$

So, the simplified expression is $c^4 - c^5$.

2. $\frac{(c^5)^{-4}}{(c^2)}$

Step 1: Simplify the expression within the parentheses: $(c^5)^{-4} = c^{-20}$

Step 2: Rewrite the expression: $\frac{c^{-20}}{c^2}$

Step 3: Negative exponent means taking the reciprocal: $\frac{1}{c^{20}} \cdot \frac{1}{c^2} = \frac{1}{c^{20+2}} = \frac{1}{c^{22}}$

So, the simplified expression is $\frac{1}{c^{22}}$.