Question

1. \\(\frac{32n^2}{24n}\\)\
2. \\(\frac{15n}{30n^3}\\)

Explanation:

Problem 4: Simplify $\boldsymbol{\frac{32n^2}{24n}}$

Step1: Simplify coefficients

Find the greatest common divisor (GCD) of 32 and 24. The GCD of 32 and 24 is 8. Divide numerator and denominator by 8:
$\frac{32\div8}{24\div8} = \frac{4}{3}$

Step2: Simplify variables

Use the exponent rule $a^m \div a^n = a^{m - n}$ for $n^2 \div n$. Here, $m = 2$, $n = 1$, so $n^{2 - 1} = n^1 = n$.

Step3: Combine results

Multiply the simplified coefficient and variable:
$\frac{4}{3} \times n = \frac{4n}{3}$

Problem 6: Simplify $\boldsymbol{\frac{15n}{30n^3}}$

Step1: Simplify coefficients

Find the GCD of 15 and 30. The GCD of 15 and 30 is 15. Divide numerator and denominator by 15:
$\frac{15\div15}{30\div15} = \frac{1}{2}$

Step2: Simplify variables

Use the exponent rule $a^m \div a^n = a^{m - n}$ for $n \div n^3$. Here, $m = 1$, $n = 3$, so $n^{1 - 3} = n^{-2} = \frac{1}{n^2}$.

Step3: Combine results

Multiply the simplified coefficient and variable:
$\frac{1}{2} \times \frac{1}{n^2} = \frac{1}{2n^2}$

Answer:

s:
Problem 4: $\boldsymbol{\frac{4n}{3}}$
Problem 6: $\boldsymbol{\frac{1}{2n^2}}$