Exponent Rules 3 - Quotient and Zero Exponent Rules Basics

Front

What is the Quotient of Powers Rule?

Back

The Quotient of Powers Rule states that when dividing two powers with the same base, you subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \).

Front

What happens when you raise a power to the power?

Back

When raising a power to another power, you multiply the exponents: \( (a^m)^n = a^{m \cdot n} \).

Front

What is the Zero Exponent Rule?

Back

The Zero Exponent Rule states that any non-zero base raised to the power of zero equals one: \( a^0 = 1 \) (where \( a \neq 0 \)).

Front

Simplify: \( \frac{a^5}{a^2} \)

Back

Using the Quotient of Powers Rule: \( \frac{a^5}{a^2} = a^{5-2} = a^3 \).

Front

Simplify: \( 10x^{-2} \)

Back

Using the Negative Exponent Rule: \( 10x^{-2} = \frac{10}{x^2} \).

Front

What is the result of any expression raised to the power of zero?

Back

Any expression (except zero) raised to the power of zero equals one: \( (5x^2y)^0 = 1 \).

Front

Simplify: \( (5^3 x^2 y^4)^0 \)

Back

Using the Zero Exponent Rule: \( (5^3 x^2 y^4)^0 = 1 \).

Front

Simplify: \( \frac{7^6}{7^{11}} \)

Back

Using the Quotient of Powers Rule: \( \frac{7^6}{7^{11}} = 7^{6-11} = 7^{-5} = \frac{1}{7^5} \).

Front

What does a negative exponent indicate?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: \( a^{-n} = \frac{1}{a^n} \).

Front

Simplify: \( c^7 \) when raised to the power of zero.

Back

Using the Zero Exponent Rule: \( c^7 \) raised to zero equals one: \( (c^7)^0 = 1 \).