Sure! To simplify the given expression step-by-step, let's analyze and break it down:
a) [tex]\(\frac{X^8 \cdot X^{-3}}{X^2 \cdot X^2}\)[/tex]
1. Simplify the Exponents in the Numerator:
Let's start with the numerator [tex]\(X^8 \cdot X^{-3}\)[/tex].
- When multiplying powers with the same base, you add the exponents: [tex]\(X^8 \cdot X^{-3} = X^{8 + (-3)} = X^5\)[/tex].
2. Simplify the Exponents in the Denominator:
Now, let's simplify the denominator [tex]\(X^2 \cdot X^2\)[/tex].
- Similarly, when multiplying powers with the same base, you add the exponents: [tex]\(X^2 \cdot X^2 = X^{2+2} = X^4\)[/tex].
3. Combine the Simplified Numerator and Denominator:
Now, we have the simplified expression:
[tex]\[
\frac{X^5}{X^4}
\][/tex]
4. Subtract the Exponents:
When dividing powers with the same base, you subtract the exponents in the denominator from the exponents in the numerator:
[tex]\[
\frac{X^5}{X^4} = X^{5-4} = X^1 = X
\][/tex]
Therefore, the simplified form of the given expression is [tex]\(X\)[/tex].
