Question

Describe how (2³) * (2⁻⁴) can be simplified.

Answer 1

The expression (2³) * (2⁻⁴) simplifies to 1/2 by adding the exponents since the bases are the same and using the rule that a negative exponent represents the inverse of the base to the positive of that exponent.

Step-by-step explanation:

The expression (2³) * (2⁻⁴) can be simplified by utilizing the properties of exponents. According to the rules for multiplying exponential quantities with the same base, we add the exponents. Here, we have 2 raised to the power of 3, multiplied by 2 raised to the negative power of 4. So, we will add the exponents: 3 + (-4).

It simplifies as follows:

1. 2³ * 2⁻⁴ = 2³⁴ (since we have the same base, we add the exponents)
2. 2³⁴ = 2-1 (adding the exponents 3 and -4 gives us -1)
3. 2-1 = 1/2¹ (a negative exponent means the inverse of the base raised to the positive of that exponent)
4. Therefore, 1/2¹ = 1/2 (simplified further to the fraction)

Thus, (2³) * (2⁻⁴) simplifies to 1/2.