Quotient and Product of Powers

Front

What is the Quotient Rule for exponents?

Back

When dividing two powers with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

What does the Product Rule state?

Back

When multiplying two powers with the same base, add the exponents: a^m * a^n = a^(m+n).

Front

Simplify: a^5 / a^2

Back

a^(5-2) = a^3.

Front

Simplify: x^7 * x^3

Back

x^(7+3) = x^10.

Front

What is the result of 2^5 / 2^3?

Back

2^(5-3) = 2^2 = 4.

Front

If a^m = 1, what can we say about m?

Back

m must be 0, since any non-zero number raised to the power of 0 is 1.

Front

What happens when you multiply a power by itself?

Back

You add the exponents: a^m * a^m = a^(m+m) = a^(2m).

Front

Evaluate: 3^4 / 3^2

Back

3^(4-2) = 3^2 = 9.

Front

What is the result of (x^3)^2?

Back

x^(3*2) = x^6.

Front

If a^0 = 1, what does this imply about a?

Back

a cannot be 0, since 0^0 is undefined.