Simplify x 675/x 453

To simplify the expression \( \frac{675}{453} \), we can start by finding the greatest common divisor (GCD) of the two numbers.

1. Finding the GCD:

   • The prime factorization of 675 is: \[ 675 = 5^2 \times 3^3 \] (since \( 675 = 25 \times 27 = 5^2 \times (3^3) \)).

   • The prime factorization of 453 is: \[ 453 = 3^2 \times 5^1 \times 7^1 \] (since \( 453 = 3 \times 151 \) and 151 is prime).

2. Identifying common factors:

   • The common prime factors of 675 and 453 are \( 3 \) with \( 3^2 \) being in the factorization of 453 and \( 3^3 \) in the factorization of 675. Therefore, the GCD is: \[ \text{GCD}(675, 453) = 3^2 = 9 \]

3. Dividing both numbers by their GCD:

   • Now, we can simplify the fraction: \[ \frac{675 \div 9}{453 \div 9} = \frac{75}{50.333} \]

4. Final simplification:

   • We can continue this to \( \frac{75 \div 3}{50 \div 3}\) which reduces to \[ \frac{25}{15} = \frac{5}{3} \]

Thus, the simplified expression for \( \frac{675}{453} \) is:

\[ \frac{225}{151} \]

I apologize for the misunderstanding. If you have \( x^{675} \) divided by \( x^{453} \), the expression can be simplified using the properties of exponents.

To simplify \( \frac{x^{675}}{x^{453}} \), you can subtract the exponent in the denominator from the exponent in the numerator:

\[ \frac{x^{675}}{x^{453}} = x^{675 - 453} \]

Now, perform the subtraction:

\[ 675 - 453 = 222 \]

So, the simplified expression is:

\[ x^{222} \]