Question

1. \\(\frac{x^4y^6}{xy^2}\\) \\(= x^3y^4\\)
2. \\(\frac{x^2y^5}{xy^4}\\) \\(x^8y^{20}\\)
3. \\(\left(\frac{4x^3y}{16xy^4}\

ight)^3\\)

1. \\(\left(\frac{5x^3y}{20xy^3}\

ight)^4\\)

1. \\(y^{-7}\\) \\(\frac{1}{y^7}\\)
2. \\(7^{-2}\\) \\(\frac{1}{7^2}\\)
3. \\(\frac{1}{x^{-5}}\\) \\(x^5\\)
4. \\(\frac{1}{2^{-4}}\\) \\(2^4\\)
5. \\(x^5 \cdot x^{-1}\\) \\(x^4\\)
6. \\(x^{-6}\\) \\(\frac{1}{x^6}\\)
7. \\(x^9 \cdot x^{-7}\\) \\(x^2\\)
8. \\((j^{-13})(j^4)(j^6)\\) \\(j^{-3}\\)
9. \\(\frac{x^{-1}}{x^{-4}}\\)
10. \\(\frac{52x^4}{13x^{-7}}\\)
11. \\(f^{-3}(f^2)(f^{-3})\\)
12. \\(\frac{x^{-4}}{x^{-9}}\\)
13. \\(\frac{24x^6}{12x^{-8}}\\)
14. \\(\frac{3x^2y^{-3}}{12x^6y^3}\\)
15. \\((2x^3y^{-3})^{-2}\\)
16. \\(\frac{2x^4y^{-4}}{8x^7y^3}\\)
17. \\((4x^4y^{-4})^3\\)
18. \\(5x^2y(2x^4y^{-3})\\)
19. \\(\left(\frac{-7a^2b^3c^0}{3a^3b^4c^3}\

ight)^{-1}\\)

1. \\(\left(\frac{-2a^3b^3c^0}{3a^2b^2c^7}\

ight)^{-2}\\)

Explanation:

Let's solve problem 27: $\frac{x^{-1}}{x^{-4}}$

Step 1: Recall the exponent rule for division

When dividing two terms with the same base, we subtract the exponents: $\frac{a^m}{a^n} = a^{m - n}$
So for $\frac{x^{-1}}{x^{-4}}$, we have $x^{-1 - (-4)}$

Step 2: Simplify the exponent

$-1 - (-4) = -1 + 4 = 3$
So the expression simplifies to $x^3$

Answer:

$x^3$