Which expression is equivalent to (4^-1)^-3
To simplify the expression (4^-1)^-3, we can start by simplifying the exponent within the parenthesis.
Since the exponent of -1 indicates taking the reciprocal, (4^-1) is equal to 1/4.
Now we can rewrite the expression as (1/4)^-3.
To simplify further, we can use a property of exponents which states that (a^-b) is equal to (1/a^b). Applying this to (1/4)^-3, we have (1/(1/4)^3).
Exponentiating 1/4 to the power of 3 means multiplying it by itself three times. So, (1/4)^3 = (1/4) * (1/4) * (1/4) = (1/64).
Therefore, (1/4)^-3 is equal to 1/(1/64), which simplifies to 64.
Hence, the expression (4^-1)^-3 is equivalent to 64.