Question

Сократить дробь ((2x)^2)/x^-15)*((x^-9)/5x^8)

Answer 1

$\frac{(2x)^2}{x^{-15}}\cdot \frac{x^{-9}}{5x^8}=\frac{4}{5}\cdot x^2\cdot x^{15}\cdot x^{-9}\cdot x^{-8}=\frac{4}{5}\cdot x^{2+15-8-9}=0.8$

Answer 2

To simplify the given expression, follow these steps:

Step 1: Combine the terms with the same base and perform the operations.

((2x)^2 / x^(-15)) * (x^(-9) / (5x^8))

Step 2: Simplify the expressions in the numerator and denominator.

In the first term, ((2x)^2 / x^(-15)), we can simplify (2x)^2 as (2x) * (2x) = 4x^2.

In the second term, x^(-9) / (5x^8), we can simplify the denominator using the rule a^m / a^n = a^(m-n). So, x^(-9) / (5x^8) = x^(-9 - 8) / 5 = x^(-17) / 5.

Step 3: Combine the simplified terms.

Now the expression becomes:

(4x^2 / x^(-15)) * (x^(-17) / 5)

Step 4: Simplify further using the rule a^m / a^n = a^(m-n).

In the first term, 4x^2 / x^(-15) = 4x^(2 - (-15)) = 4x^17.

So, the expression becomes:

4x^17 * (x^(-17) / 5)

Step 5: Simplify the expression in the parentheses.

In the second term, x^(-17) / 5, we can rewrite the negative exponent as 1 / x^17.

So, the expression becomes:

4x^17 * (1 / 5x^17)

Step 6: Cancel out the common factors.

The common factor x^17 in the numerator and denominator can be canceled out:

4 * (1 / 5) = 4/5.

Therefore, the simplified expression is:

4/5.