This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to problems 21-36:
Step 21: Simplify $\frac{z^2}{z}$
$$ \frac{z^2}{z} = z^{2-1} = z $$
The simplified expression is $\boxed{z}$.
Step 22: Simplify $\frac{3x^2}{x}$
$$ \frac{3x^2}{x} = 3x^{2-1} = 3x $$
The simplified expression is $\boxed{3x}$.
Step 23: Simplify $6x^2 \div x$
$$ 6x^2 \div x = \frac{6x^2}{x} = 6x^{2-1} = 6x $$
The simplified expression is $\boxed{6x}$.
Step 24: Simplify $\frac{5c^2}{c}$
$$ \frac{5c^2}{c} = 5c^{2-1} = 5c $$
The simplified expression is $\boxed{5c}$.
Step 25: Simplify $\frac{3x^3}{x}$
$$ \frac{3x^3}{x} = 3x^{3-1} = 3x^2 $$
The simplified expression is $\boxed{3x^2}$.
Step 26: Simplify $\frac{2x^3}{x}$
$$ \frac{2x^3}{x} = 2x^{3-1} = 2x^2 $$
The simplified expression is $\boxed{2x^2}$.
Step 27: Simplify $\frac{5x^3}{x^2}$
$$ \frac{5x^3}{x^2} = 5x^{3-2} = 5x $$
The simplified expression is $\boxed{5x}$.
Step 28: Simplify $\frac{12x^3}{3x}$
$$ \frac{12x^3}{3x} = \frac{12}{3} \times \frac{x^3}{x} = 4x^{3-1} = 4x^2 $$
The simplified expression is $\boxed{4x^2}$.
Step 29: Simplify $\frac{18a^3}{3a}$
$$ \frac{18a^3}{3a} = \frac{18}{3} \times \frac{a^3}{a} = 6a^{3-1} = 6a^2 $$
The simplified expression is $\boxed{6a^2}$.
Step 30: Simplify $\frac{26x^2}{2x}$
$$ \frac{26x^2}{2x} = \frac{26}{2} \times \frac{x^2}{x} = 13x^{2-1} = 13x $$
The simplified expression is $\boxed{13x}$.
Step 31: Simplify $\frac{33mn}{8a}$
$$ \frac{33mn}{8a} $$
The expression cannot be simplified further as there are no common factors in the numerator and denominator. The simplified expression is $\boxed{\frac{33mn}{8a}}$.
Step 32: Simplify $\frac{42xy}{7y}$
$$ \frac{42xy}{7y} = \frac{42}{7} \times \frac{xy}{y} = 6x $$
The simplified expression is $\boxed{6x}$.
Step 33: Simplify $\frac{54ab}{9b}$
$$ \frac{54ab}{9b} = \frac{54}{9} \times \frac{ab}{b} = 6a $$
The simplified expression is $\boxed{6a}$.
Step 34: Simplify $\frac{72a^2b}{8a}$
$$ \frac{72a^2b}{8a} = \frac{72}{8} \times \frac{a^2b}{a} = 9a^{2-1}b = 9ab $$
The simplified expression is $\boxed{9ab}$.
Step 35: Simplify $\frac{48x^2y}{12xy}$
$$ \frac{48x^2y}{12xy} = \frac{48}{12} \times \frac{x^2y}{xy} = 4x^{2-1}y^{1-1} = 4x $$
The simplified expression is $\boxed{4x}$.
Step 36: Simplify $\frac{40pq^2}{8pq}$
$$ \frac{40pq^2}{8pq} = \frac{40}{8} \times \frac{pq^2}{pq} = 5p^{1-1}q^{2-1} = 5q $$
The simplified expression is $\boxed{5q}$.
That's 2 down. 3 left today — send the next one.