Which of the following is equivalent to 6^−2 ?(1 point) Responses 136 Start Fraction 1 over 36 End Fraction 126 Start Fraction 1 over 2 superscript 6 baseline End Fraction 16−2 Start Fraction 1 over 6 superscript negative 2 baseline End Fraction 36
The equivalent expression to 6^−2 is Start Fraction 1 over 6 superscript negative 2 baseline End Fraction
To find the value of 6^(-2), we need to take the reciprocal of 6^2. The reciprocal of a number x is 1/x.
Therefore, 6^(-2) is equivalent to 1/6^2.
Simplifying 6^2, we get 36.
Hence, 6^(-2) is equivalent to 1/36.
So, the correct response is "Start Fraction 1 over 36 End Fraction".
To find the value equivalent to 6^(-2), we need to understand the concept of negative exponents.
In general, a negative exponent indicates that the base should be inverted (taken reciprocal) and raised to the positive power. So, 6^(-2) can be rewritten as 1/(6^2).
Now, let's calculate 6^2, which is equal to 6 * 6 = 36.
So, 1/(6^2) is equal to 1/36.
Therefore, the correct answer is "Start Fraction 1 over 36 End Fraction".