Answer :
Let's simplify the expression [tex]\(\frac{5x^6 \cdot 7x^7}{28x^8}\)[/tex] step-by-step.
1. Combine the terms in the numerator:
- Multiply the coefficients: [tex]\(5 \times 7 = 35\)[/tex].
- Add the exponents of [tex]\(x\)[/tex] since we are multiplying like terms: [tex]\(x^6 \times x^7 = x^{6+7} = x^{13}\)[/tex].
- So, the numerator becomes [tex]\(35x^{13}\)[/tex].
2. Rewrite the denominator:
- The denominator is already in a simplified form as [tex]\(28x^8\)[/tex].
3. Simplify the fraction:
- Divide the coefficients: [tex]\(\frac{35}{28}\)[/tex]. This simplifies to [tex]\(\frac{5}{4}\)[/tex] after dividing both the numerator and the denominator by their greatest common divisor, which is 7.
- Simplify the exponents of [tex]\(x\)[/tex]: [tex]\(\frac{x^{13}}{x^8} = x^{13-8} = x^5\)[/tex].
4. Write the final simplified expression:
- Combining the simplified coefficient and the power of [tex]\(x\)[/tex], the expression is [tex]\(\frac{5}{4}x^5\)[/tex].
Therefore, the simplified expression is [tex]\(\frac{5}{4}x^5\)[/tex].
1. Combine the terms in the numerator:
- Multiply the coefficients: [tex]\(5 \times 7 = 35\)[/tex].
- Add the exponents of [tex]\(x\)[/tex] since we are multiplying like terms: [tex]\(x^6 \times x^7 = x^{6+7} = x^{13}\)[/tex].
- So, the numerator becomes [tex]\(35x^{13}\)[/tex].
2. Rewrite the denominator:
- The denominator is already in a simplified form as [tex]\(28x^8\)[/tex].
3. Simplify the fraction:
- Divide the coefficients: [tex]\(\frac{35}{28}\)[/tex]. This simplifies to [tex]\(\frac{5}{4}\)[/tex] after dividing both the numerator and the denominator by their greatest common divisor, which is 7.
- Simplify the exponents of [tex]\(x\)[/tex]: [tex]\(\frac{x^{13}}{x^8} = x^{13-8} = x^5\)[/tex].
4. Write the final simplified expression:
- Combining the simplified coefficient and the power of [tex]\(x\)[/tex], the expression is [tex]\(\frac{5}{4}x^5\)[/tex].
Therefore, the simplified expression is [tex]\(\frac{5}{4}x^5\)[/tex].
