Question

Simplify x 675/x 453

Answer 1

its x to the power 675 and x to the power of 453

Answer 2

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:

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

Answer 3

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:

\[
x^{222}
\]