Real Numbers, Exponent Rules, and Algebraic Simplification

Rational Number

A number that can be expressed as a ratio or fraction $\frac{a}{b}$ of two integers, where $b \neq 0$.

Irrational Number

A real number that cannot be expressed as a simple fraction of two integers; its decimal representation is non-terminating and non-repeating.

Statement A (Truth Value)

False: The product of $\sqrt{6} \cdot \sqrt{6} = 6$, which is rational.

Statement B (Truth Value)

True: $\frac{40}{2}$ simplifies to 20, which is an integer.

Statement C (Truth Value)

True: Natural numbers are a subset of rational numbers.

Coefficient Comparison

In the equation $9A = -36$, solve for A to get $A = -4$.

Algebraic Exponents (Product Rule)

$a^m \cdot a^n = a^{m+n}$.

Algebraic Exponents (Quotient Rule)

$\frac{a^m}{a^n} = a^{m-n}$.

Algebraic Exponents (Power of a Product Rule)

$(ab)^n = a^n b^n$.

Simplification Example

For $\frac{42h^2}{28h^{11}}$, simplification gives $\frac{3}{2h^9}$.

Final Parameter Values

$A = -4$, $B = 2$, $C = 9$ in the problem statement.