Question

$(\frac{1}{2})^3\times(\frac{1}{2})^4\times(\frac{1}{2})^5= ?$

• A. 1/256
• B. 1/512
• C. 1/4096
• D. 1/2024

Answer 1

Answer:

C. 1/4096

The correct answer is $\frac{1}{4096}$ (or $2^{-12}$).

## 1. Apply the Law of Exponents

When you multiply numbers with the same base, you add their exponents together:

$a^m \times a^n \times a^p = a^{m + n + p}$

Using our base $\frac{1}{2}$:

$\left(\frac{1}{2}\right)^3 \times \left(\frac{1}{2}\right)^4 \times \left(\frac{1}{2}\right)^5 = \left(\frac{1}{2}\right)^{3 + 4 + 5}$

$\left(\frac{1}{2}\right)^{12}$

## 2. Solve the Final Exponent

Distribute the power of 12 to both the numerator and the denominator:

$\frac{1^{12}}{2^{12}}$

* $1^{12} = 1$

* $2^{12} = 4096$

$\frac{1}{4096}$