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
.

1x⋅1x⋅1x⋅1x⋅1x⋅1x\frac{1}{x}\cdot\frac{1}{x}\cdot\frac{1}{x}\cdot\frac{1}{x}\cdot\frac{1}{x}\cdot\frac{1}{x}
x
1
​
⋅
x
1
​
⋅
x
1
​
⋅
x
1
​
⋅
x
1
​
⋅
x
1
​

Answer 1

To simplify the expression \( \frac{1}{x} \cdot \frac{1}{x} \cdot \frac{1}{x} \cdot \frac{1}{x} \cdot \frac{1}{x} \cdot \frac{1}{x} \), we can first rewrite it using powers.

Since we are multiplying six fractions of \( \frac{1}{x} \), we can express this as:

\[ \left( \frac{1}{x} \right)^6 \]

Using the properties of exponents, we can simplify \( \left( \frac{1}{x} \right)^6 \) to:

\[ \frac{1^6}{x^6} = \frac{1}{x^6} \]

Now, to express it with positive exponents, we can rewrite \( \frac{1}{x^6} \) as:

\[ x^{-6} \]

However, since the instructions require that we write it in exponential form with positive exponents only, we express the negative exponent according to the guidelines:

\[ \frac{1}{x^6} \]

So, the final simplified form of the expression in positive exponent form is:

\[ \frac{1}{x^6} \]