Question

Помогите решить 81*3в 6 степени ----------------------- (3в 4 степени)в 3 степени ответ знаю одна девятая Решите с помощью форм и объясните

Answer 1

Уверен,что одна 9?
$\frac{9 ^{2} *3 ^{6} }{3 ^{7} } = \frac{27 ^{8} }{3 ^{12} } = \frac{27}{3^2}= \frac{27}{81} = \frac{3}{9}$

Answer 2

Solving the Exponential Expression

To solve the given expression 81*3^6 / (3^4)^3, we can use the properties of exponents. Let's break it down step by step.

First, let's simplify the expression 81*3^6: - 81 can be expressed as 3^4 because 3^4 = 81. - So, 81*3^6 becomes 3^4 * 3^6. - According to the properties of exponents, when multiplying with the same base, we add the exponents. Therefore, 3^4 * 3^6 equals 3^(4+6).

Now, let's simplify the expression (3^4)^3: - According to the properties of exponents, when raising a power to another power, we multiply the exponents. Therefore, (3^4)^3 equals 3^(4*3).

So, the original expression becomes 3^(4+6) / 3^(4*3).

Applying Exponent Properties

Now, let's apply the properties of exponents to simplify the expression further.

- 3^(4+6) can be simplified to 3^10. - 3^(4*3) can be simplified to 3^12.

So, the expression simplifies to 3^10 / 3^12.

Final Calculation

To simplify 3^10 / 3^12, we can use the property that when dividing with the same base, we subtract the exponents. Therefore, 3^10 / 3^12 equals 3^(10-12), which is 3^(-2).

So, the final answer is 1 / 3^2, which equals 1 / 9.

Therefore, the solution to the expression 81*3^6 / (3^4)^3 is 1/9.

This explanation is based on the properties of exponents and the simplification of exponential expressions.