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: \( \frac{a^m}{a^n} = a^{m-n} \).

Tags

CCSS.8.EE.A.1

Front

What happens when you raise a power to the power?

Back

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

Tags

CCSS.8.EE.A.1

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 \( a \neq 0 \)).

Tags

CCSS.8.EE.A.1

Front

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

Back

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

Tags

CCSS.8.EE.A.1

Front

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

Back

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

Tags

CCSS.8.EE.A.1

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: \( (5x^2y)^0 = 1 \).

Tags

CCSS.8.EE.A.1

Front

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

Back

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

Tags

CCSS.8.EE.A.1

Front

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

Back

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

Tags

CCSS.8.EE.A.1

Front

What does a negative exponent indicate?

Back

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

Tags

CCSS.8.EE.A.1

Front

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

Back

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

Tags

CCSS.8.EE.A.1