Question

(3/2^-4):(2^3) ^-степень

Answer 1

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Answer 2

To simplify the expression (3/2^-4):(2^3) ^-степень, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right).

Let's break down the expression step by step:

1. Start by simplifying the exponent in the denominator: (2^3)^-степень = 2^(3 * степень) = 2^(3 * степень).

2. Rewrite the expression: (3/2^-4) / 2^(3 * степень).

3. Apply the negative exponent to the numerator: 2^-4 = 1/2^4.

4. Rewrite the expression: (3/(1/2^4)) / 2^(3 * степень).

5. Invert the denominator and rewrite the expression: (3 * 2^4) / 2^(3 * степень).

6. Simplify the numerator: 3 * 2^4 = 3 * 16 = 48.

7. Rewrite the expression: 48 / 2^(3 * степень).

8. Since the exponent of 2 is raised to another exponent, we multiply the exponents: 2^(3 * степень) = 2^(3степень).

9. Final expression: 48 / 2^(3степень).

Therefore, the simplified expression is 48 / 2^(3степень).