Answer: D) 32
Explanation:
To solve the expression (4 to the negative power of 1)(2 to the 3rd power divided by 4 to the negative power of 2), we can follow these steps:
Step 1: Simplify 4 to the negative power of 1
4 to the negative power of 1 can be written as 1/4 to the positive power of 1, so the expression becomes: (1/4)(2 to the 3rd power divided by 4 to the negative power of 2)
Step 2: Simplify the division of powers of 4
When dividing powers with the same base (in this case, 4), we can subtract the exponents. So, 4 to the negative power of 2 is the same as 1/4 to the power of 2, which equals 1/16. The expression now becomes: (1/4)(2 to the 3rd power divided by 1/16)
Step 3: Simplify 2 to the 3rd power 2 to the 3rd power is 2x2x2, which equals 8. The expression now becomes: (1/4)(8 divided by 1/16)
Step 4: Simplify the division
Dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression as: (1/4)(8 x 16)
Step 5: Multiply 8 x 16 equals 128, so the expression simplifies to: (1/4)(128)
Step 6: Simplify the final expression
Multiplying 1/4 by 128 gives us 32. Therefore, the final answer is: 32