Question

What is the value of 64 raised to the power of negative two as a fraction?

A) 1/64
B) 1/4096
C) 1/256
D) 1/16

Answer 1

The value of 64 raised to the power of negative two as a fraction is 1/4096, which involves squaring the number 64 and then taking the reciprocal due to the negative exponent. b is correct.

Step-by-step explanation:

To find the value of 64 raised to the power of negative two as a fraction, we first need to understand the concept of negative exponents. A negative exponent indicates that the number should be taken as the reciprocal and then raised to the absolute value of the given exponent. Therefore, 64 to the power of -2 implies 1 divided by 64 squared.

Let's calculate it step by step:

1. Compute 64 squared: 64 × 64 = 4096.
2. Take the reciprocal for the negative exponent: 1 / 4096.

So, the value of 64 raised to the power of negative two as a fraction is 1/4096, which corresponds to the mention correct option B) 1/4096.