Question

Как из 49^-6 получилось 7^-12?

Answer 1

$= (7^{2}) ^{-6}= 7^{2*(-6)}= 7^{-12}$

Answer 2

Calculation of 49^-6 and 7^-12

To understand how 49^-6 can be equal to 7^-12, let's break down the calculation step by step.

First, let's simplify 49^-6. The negative exponent indicates that we need to take the reciprocal of the base raised to the positive exponent. In this case, the base is 49 and the positive exponent is 6. So, 49^-6 can be written as 1/49^6.

Next, let's simplify 1/49^6. To calculate this, we need to raise 49 to the power of 6 and then take the reciprocal of the result.

Calculating 49^6: 49^6 = 49 * 49 * 49 * 49 * 49 * 49 = 117,649 * 117,649 = 13,841,287,201.

Taking the reciprocal of 13,841,287,201: 1/13,841,287,201 ≈ 7.2202 * 10^-11.

Therefore, 49^-6 is approximately equal to 7.2202 * 10^-11.

Now, let's move on to 7^-12. Similarly, the negative exponent indicates that we need to take the reciprocal of the base raised to the positive exponent. In this case, the base is 7 and the positive exponent is 12. So, 7^-12 can be written as 1/7^12.

Calculating 7^12: 7^12 = 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 * 7 = 19,487,171.

Taking the reciprocal of 19,487,171: 1/19,487,171 ≈ 5.1344 * 10^-13.

Therefore, 7^-12 is approximately equal to 5.1344 * 10^-13.

To summarize, the calculations show that 49^-6 is approximately equal to 7.2202 * 10^-11, and 7^-12 is approximately equal to 5.1344 * 10^-13. These values are not equal to each other.