Final answer:
The value of (11^(-1))^3 is found by multiplying the exponents, resulting in 11^(-3), which is the reciprocal of 11 cubed, giving us 1/1331 or (B) 1/11 cubic.
Step-by-step explanation:
The value of (11^(-1))^3 is found by multiplying the exponents, resulting in 11^(-3), which is the reciprocal of 11 cubed, giving us 1/1331 or (B) 1/11 cubic. The question asks for the value of (11^(-1))^3. To solve this, we need to understand the properties of exponents.
When an exponent is raised to another power, as is the case here, you multiply the exponents. So the expression (11^(-1))^3 becomes 11^(-1*3), which is 11^(-3). The negative exponent indicates that the base (11) should be taken as the reciprocal. Thus, 11^(-3) is the same as 1/(11^3). So the final answer is 1/11^3, which is 1/1331, or (B) 1/11 if we were looking at 11^(-1) and then cubing the result (1/11)^3, which is still 1/1331.