EXPONENT RULES

Front

What is the Quotient Rule for Exponents?

Back

When dividing two powers with the same base, subtract the exponents: \( \frac{a^m}{a^n} = a^{m-n} \)

Front

What is the Product Rule for Exponents?

Back

When multiplying two powers with the same base, add the exponents: \( a^m \cdot a^n = a^{m+n} \)

Front

What is any non-zero number raised to the power of zero?

Back

Any non-zero number raised to the power of zero is equal to 1: \( a^0 = 1 \) for \( a \neq 0 \)

Front

What is the value of \( \frac{7^3}{7^{10}} \)?

Back

The value is \( \frac{1}{7^7} \) using the Quotient Rule.

Front

What is the value of \( \frac{5^3}{5^2} \)?

Back

The value is \( 5 \) using the Quotient Rule.

Front

What happens when you raise a power to another power?

Back

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

Front

What is the value of \( (877237646642375623646237)^0 \)?

Back

The value is 1, since any non-zero number raised to the power of zero is 1.

Front

How do you simplify \( a^m \cdot a^n \)?

Back

You simplify it by adding the exponents: \( a^m \cdot a^n = a^{m+n} \)

Front

How do you simplify \( a^m \div a^n \)?

Back

You simplify it by subtracting the exponents: \( a^m \div a^n = a^{m-n} \)

Front

What is the result of \( 2^3 \cdot 2^2 \)?

Back

The result is \( 2^5 \) because you add the exponents.