Question

Simplify 2-8 × 2-4.
a) 22²²
b) 1.232
c) 1.24¹.²
d) 2⁻¹²

Answer 1

To simplify 2^-8 × 2^-4, apply the law of exponents to add the exponents since the base is the same, resulting in 2^-12. If the provided options include a corrected option d) as 2^-12, this would be the correct choice.

Step-by-step explanation:

The student is asking how to simplify 2-8 × 2-4. This involves understanding the laws of exponents, which tell us that when we multiply powers with the same base, we add the exponents. Therefore, we have:

• 2-8 × 2-4 = 2-8 + (-4)
• 2-8 × 2-4 = 2-12

In standard notation, 2-12 can be expressed as 1/212 or approximated as a decimal 0.000244, which is not one of the listed options. If we correct the possible typo in option d) to 2-12 instead of 2⁻¹², then the correct answer would be d) 2-12.