Which of the following is equivalent to 2^−4? (1 point)
A. 1/2^-4
B. 1/16
C. 16
D. 1/2
A. 1/2^-4
To find the equivalent expression for 2^(-4), we can use the definition of negative exponents.
The definition states that a^(-n) is equal to 1 divided by a^n.
So, 2^(-4) is equal to 1 divided by 2^(4).
Therefore, the correct option is A. 1/2^(-4).
To find the equivalent value of 2^−4, we need to understand the concept of negative exponents.
When we have a negative exponent, it means that we need to take the reciprocal of the base raised to the positive exponent. In this case, 2^−4 means the reciprocal of 2^4.
To find the reciprocal, we can simply take the fraction 1 divided by the base raised to the positive exponent. Therefore, 2^−4 is equivalent to 1/2^4.
Now, let's check the given options:
A. 1/2^-4: We already determined that this is the equivalent expression for 2^−4, so it is a correct equivalent form.
B. 1/16: This is not the same as 1/2^4. Therefore, it is not equivalent to 2^−4.
C. 16: This is not the same as 1/2^4. Therefore, it is not equivalent to 2^−4.
D. 1/2: This is not the same as 1/2^4. Therefore, it is not equivalent to 2^−4.
From the given options, the correct equivalent expression for 2^−4 is A. 1/2^-4.