Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}

Question

5
3

1
​
not 5−35^{-3}5
−3
.
2^-7 * 2* 2^-4

Answer 1

To simplify the expression \(2^{-7} \cdot 2 \cdot 2^{-4}\), we can use the property of exponents which states that when multiplying numbers with the same base, you add their exponents.

Let's rewrite \(2\) as \(2^1\):

\[ 2^{-7} \cdot 2^1 \cdot 2^{-4} \]

Now we can add the exponents:

\[ -7 + 1 - 4 = -10 \]

So, we have:

\[ 2^{-10} \]

Now, to express this with positive exponents, we use the property that \(a^{-n} = \frac{1}{a^n}\):

\[ 2^{-10} = \frac{1}{2^{10}} \]

Thus, the fully simplified form of the expression \(2^{-7} \cdot 2 \cdot 2^{-4}\) in exponential form with positive exponents is:

\[ \frac{1}{2^{10}} \]