4-3: Multiplication and Division Properties of Exponents

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 is the product rule for exponents?

Back

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

Front

How do you simplify 5^16 / 5^4?

Back

Using the quotient rule, 5^16 / 5^4 = 5^(16-4) = 5^12.

Front

How do you simplify 5^5 * 5^9?

Back

Using the product rule, 5^5 * 5^9 = 5^(5+9) = 5^14.

Front

What happens when you divide two powers with different bases?

Back

You cannot simplify them using the exponent rules; you must leave them as is.

Front

Can you combine m^10 / d^3?

Back

No, you cannot combine them because they have different bases.

Front

What is the result of 5^3 * 7^3?

Back

You cannot combine them into a single power because they have different bases.

Front

How do you simplify 12^3 * 12^-2?

Back

Using the product rule, 12^3 * 12^-2 = 12^(3 + (-2)) = 12^1 = 12.

Front

What is the zero exponent rule?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1.

Front

What is the negative exponent rule?

Back

A negative exponent indicates the reciprocal: a^-n = 1/a^n.