Which expression is equivalent to $$ \frac{2^{-7} \cdot 2^{6}}{2^{0}} ? $$ Answer $$ \begin{array}{ll}0 & 2^{-42} \ 2^{-1} & 1\end{array} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \frac{2^{-7} \cdot 2^{6}}{2^{0}} $$, let's follow the rules of exponents step by step.

### Step 1: Simplify the Numerator

When multiplying powers with the same base, you add the exponents:

$$
2^{-7} \cdot 2^{6} = 2^{-7 + 6} = 2^{-1}
$$

### Step 2: Simplify the Denominator

Any number raised to the power of 0 is 1:

$$
2^{0} = 1
$$

### Step 3: Divide the Simplified Numerator by the Denominator

$$
\frac{2^{-1}}{1} = 2^{-1}
$$

### Final Answer

The expression $$ \frac{2^{-7} \cdot 2^{6}}{2^{0}} $$ simplifies to:

$$
2^{-1}
$$

### Matching with Provided Options

Given the options:

$$
\begin{array}{ll}
0 & 2^{-42} \
2^{-1} & 1
\end{array}
$$

The correct equivalent expression is **$$2^{-1}$$**.
The expression simplifies to $$2^{-1}$$.

Which expression is equivalent to
Answer