Question

Вычислите : (0.2)³ * (0.2²)³ ------------------- == (0.2)⁸

Answer 1

$\frac{(0.2)^3*(0.2^2)^3}{(0.2)^8} = \frac{0.2^3*0.2^6}{0.2^8} = \frac{0.2^9}{0.2^8} =0.2$

Answer 2

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To solve this problem, we need to apply the following rules of exponents:

- $(a^b)^c = a^{bc}$ - $a^b \cdot a^c = a^{b+c}$ - $\frac{a^b}{a^c} = a^{b-c}$

Using these rules, we can simplify the expression as follows:

$$\frac{(0.2)^3 \cdot (0.2^2)^3}{(0.2)^8} = \frac{(0.2)^3 \cdot (0.2)^6}{(0.2)^8} = \frac{(0.2)^{3+6}}{(0.2)^8} = \frac{(0.2)^9}{(0.2)^8} = (0.2)^{9-8} = (0.2)^1 = 0.2$$

Therefore, the answer is 0.2.

You can also use online calculators to check your answer or get more detailed steps. Here are some links that might be useful:

- [Math Calculator - Mathway | Algebra Problem Solver](https://www.mathway.com/Calculator/math-calculator) - [Math Solver - GeoGebra](https://www.geogebra.org/solver) - [Calculadora passo a passo - Symbolab](https://pt.symbolab.com/solver)