Definition: Zero Exponent Rule

Zero Exponent Rule: The Zero Exponent Rule states that any the nonzero number raised to the power of zero is equal to 1.

Explanation:

In simple terms, anything raised to the power of zero is always 1. Mathematically, if a is any non-zero real number, then:

\$a^0\$ = 1

Definition: Product of Powers Rule

Product of Powers Rule: The Product of Powers Rule states that when you have a product of two numbers raised to the same exponent, you can find the result by raising each individual factor to that exponent.

Explanation:

when you have the product (ab) raised to a certain power (n), you can simply distribute the power to both 'a' and 'b' individually.

\$ (ab)^n = a^n \times b^n\$

Definition: Quotient of Powers Rule

Quotient of Powers Rule: The Quotient of Power Rule states that when you have a fraction raised to a certain power, you can distribute that power to both the numerator and the denominator of the fraction.

Explanation:

The rule is expressed as follows:

\$ (a/b)^n = (a^n)/(b^n) \$

Here:
a and b are nonzero real numbers,
n is any real number.