Final answer:
To evaluate the expression 4^-3×4^0, we find that 4^0 equals 1 and 4^-3 equals 1/4^3, which is 1/64. Thus, the final answer to the expression is 1/64.
Step-by-step explanation:
The question asks us to evaluate the expression 4-3×40. When evaluating expressions with exponents, there are a couple of rules we need to remember.
First, any number raised to the power of 0 is 1, so 40 = 1.
Second, a negative exponent means that the base should be taken as the reciprocal and then raised to the corresponding positive exponent. Thus, 4-3 means 1/43.
To evaluate 1/43, we cube the number 4, resulting in 4×4×4 = 64. Therefore, 1/43 equals 1/64.
Combining these rules, we calculate the original expression as follows:
4-3×40 = (1/43)×1 = 1/64 × 1 = 1/64
So the final answer is 1/64.