To simplify [tex]\( \frac{3 x^8 y^3}{3 x^7 y^3} \)[/tex] using only positive exponents, follow these steps:
1. Cancel out common factors in the numerator and the denominator:
The factor of 3 appears in both the numerator and the denominator, so it can be canceled out:
[tex]\[
\frac{3 x^8 y^3}{3 x^7 y^3} = \frac{x^8 y^3}{x^7 y^3}
\][/tex]
2. Separate the expression into individual factors:
Now, treat the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] terms separately:
[tex]\[
\frac{x^8 y^3}{x^7 y^3} = \frac{x^8}{x^7} \cdot \frac{y^3}{y^3}
\][/tex]
3. Simplify the y terms:
[tex]\(\frac{y^3}{y^3}\)[/tex] is equal to 1 (since any non-zero term divided by itself is 1):
[tex]\[
\frac{y^3}{y^3} = 1
\][/tex]
4. Simplify the x terms using the properties of exponents:
When dividing like bases, you subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
\frac{x^8}{x^7} = x^{8-7} = x^1 = x
\][/tex]
5. Combine the results:
Putting it all together, we have:
[tex]\[
\frac{x^8 y^3}{x^7 y^3} = x \cdot 1 = x
\][/tex]
Final simplified expression:
[tex]\[
\boxed{x}
\][/tex]
