To simplify the expression you provided, we need to rewrite it properly using the properties of integer exponents.
The expression seems to be:
\[ (7^3)^{7^{20}} / 6 - 2 \]
Now let's apply the properties of exponents.
- First, simplify \( (7^3)^{7^{20}} \).
Using the power of a power property, which states that \( (a^m)^n = a^{m \cdot n} \), we get:
\[ (7^3)^{7^{20}} = 7^{3 \cdot 7^{20}} \]
-
The goal now is to simplify \( 7^{3 \cdot 7^{20}} \):
- We can manipulate the exponents further. Since \( 7^{20} = 7 \times 7^{19} \), we can multiply the exponents:
\[ 3 \cdot 7^{20} = 3 \times 7^{20} \]
Thus, we can express the number simply as \( 7^{(3 \cdot 7^{20})} \).
- To address the division by 6, we can rewrite our expression:
\[ \frac{7^{(3 \cdot 7^{20})}}{6} - 2 \]
But we want to express the answer as an improper fraction, we have \( \frac{7^{(3 \cdot 7^{20})}}{6} \).
To show that the resulting expression minus 2 can also be expressed as an improper fraction, we will represent 2 as a fraction:
\[ 2 = \frac{12}{6} \]
Thus, our entire expression becomes:
\[ \frac{7^{(3 \cdot 7^{20})}}{6} - \frac{12}{6} = \frac{7^{(3 \cdot 7^{20})} - 12}{6} \]
Now the expression has been converted to an improper fraction format.
In the simplified form, we find that the numerator is \( 7^{(3 \cdot 7^{20})} - 12 \).
Since \( 7^{(3 \cdot 7^{20})} \) is a huge value from the exponentiation, it definitely gives a very large integer.
Thus, the answer in improper fraction form to your original expression can be given as:
\[ \frac{7^{(3 \cdot 7^{20})} - 12}{6} \]
This format now represents the answer as an improper fraction, with the numerator being \( 7^{(3 \cdot 7^{20})} - 12 \) and the denominator 6.
9 answers