Why is 6^-2 not equivalent to 1/6^-2
To understand why 6^-2 is not equivalent to 1/6^-2, let's evaluate both expressions separately.
First, let's simplify 6^-2. The exponent -2 means to take the reciprocal of the base raised to the positive exponent 2. So, 6^-2 is equal to 1/6^2.
6^2 means 6 multiplied by itself (6 * 6) = 36. Thus, 6^(-2) = 1/36.
Now, let's simplify 1/6^-2. Again, the exponent -2 means to take the reciprocal of the base raised to the positive exponent 2. So, 1/6^-2 is equal to 1/(1/6^2).
(1/6^2) means 1 divided by 6 multiplied by itself (1 / (6 * 6)) = 1/36.
So, both expressions are indeed equivalent. 6^-2 and 1/6^-2 both equal 1/36.
To understand why 6^-2 is not equivalent to 1/6^-2, let's break down the calculations step-by-step.
First, let's calculate 6^-2.
The exponent -2 means that we need to take the inverse or reciprocal of the base, which is 6 in this case, and then square it.
So, 6^-2 can be calculated as:
6^-2 = 1/(6^2)
= 1/36
Now, let's calculate 1/6^-2.
Here, the exponent -2 is applied to the denominator (6). To calculate the reciprocal of 6 raised to the power of -2, we need to take the inverse or reciprocal of the base, which is 6, and then square it.
So, 1/6^-2 can be calculated as:
1/6^-2 = 1/(1/(6^2))
= 1/1/36
= 36
Therefore, we can see that 6^-2 is equal to 1/36, while 1/6^-2 is equal to 36. Therefore, they are not equivalent.
To understand why 6^-2 is not equivalent to 1/6^-2, let's first simplify each expression separately.
The exponent '-2' implies taking the reciprocal of the base raised to the positive exponent '2'. So, 6^-2 can be calculated as 1/6^2, which is equal to 1/36.
On the other hand, the expression 1/6^-2 can be simplified by applying the rule that states when dividing two numbers with the same base but different exponents, we subtract the exponents. In this case, the base is 6, and the exponents are 0 (implied) and -2. So, 1/6^-2 can be rewritten as 1/6^0 * 6^2.
Now, any number raised to the power of 0 is always equal to 1. Therefore, 6^0 equals 1 (anything raised to the power of 0 is equal to 1). Consequently, 1/6^0 * 6^2 simplifies to 1 * 6^2, which is equal to 36.
Hence, 6^-2 is equal to 1/36, while 1/6^-2 is equal to 36. These two expressions are not equivalent.