Question

Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3} 5 3 1 ​ not 5−35^{-3}5 −3 . Click Here for Help Video. 1𝑧6⋅1𝑧6=\frac{1}{z^{6}}\cdot\frac{1}{z^{6}}= z 6 1 ​ ⋅ z 6 1 ​ =

Answer 1

To simplify the expression \( \frac{1}{z^6} \cdot \frac{1}{z^6} \), you can follow these steps:

1. First, rewrite the expression using the multiplication of the fractions:
\[
\frac{1}{z^6} \cdot \frac{1}{z^6} = \frac{1 \cdot 1}{z^6 \cdot z^6}
\]

2. The product of \( z^6 \cdot z^6 \) can be simplified using the property of exponents:
\[
z^6 \cdot z^6 = z^{6+6} = z^{12}
\]

3. Therefore, the expression becomes:
\[
\frac{1}{z^{12}}
\]

4. To write this with a positive exponent, you can rewrite the fraction as:
\[
z^{-12}
\]

So, the fully simplified form of your original expression \( \frac{1}{z^6} \cdot \frac{1}{z^6} \) is
\[
z^{-12}.
\]

However, since the problem asks for positive exponents only, you would typically express it as:
\[
\frac{1}{z^{12}}.
\]

Thus, the final answer in exponent form with positive exponents is:
\[
\frac{1}{z^{12}}.
\]