Question

1/2 to the negative 6th power?

Answer 1

64

Explanation:

Negative exponents can be simplified using exponent rules.

Negative Exponents

The negative exponent rule states that
`\displaystyle a^(-n) =(1)/(a^(n) )`. This means that a negative exponent can be simplified by taking the reciprocal. Once the exponent is simplified, it will become positive and can be solved normally.

Solving For the Answer

Now we can solve the problem we were given. First, take the reciprocal.

• 
  `\displaystyle (1)/(2)^(-6) =2^(6)`

Then, just raise 2 to the 6th power.

• 
  `2^(6)=64`

This means that 1/2 to the negative 6th power is 64.