Product of Powers

Front

What is the Product of Powers property in exponents?

Back

The Product of Powers property states that when multiplying two powers with the same base, you add the exponents. For example, a^m * a^n = a^(m+n).

Front

How do you simplify y^4 * y^{-2}?

Back

Using the Product of Powers property, y^4 * y^{-2} = y^(4 + (-2)) = y^2.

Front

What is the result of 12^3 * 12?

Back

Using the Product of Powers property, 12^3 * 12 = 12^(3 + 1) = 12^4.

Front

How do you simplify 2^5 * 2^3?

Back

Using the Product of Powers property, 2^5 * 2^3 = 2^(5 + 3) = 2^8.

Front

What is the value of 5^{1/2} * 5^{1/2}?

Back

Using the Product of Powers property, 5^{1/2} * 5^{1/2} = 5^{(1/2 + 1/2)} = 5^1 = 5.

Front

How do you simplify 7^{1/6} * 7^{2/3}?

Back

Using the Product of Powers property, 7^{1/6} * 7^{2/3} = 7^{(1/6 + 4/6)} = 7^{5/6}.

Front

What is the general formula for the Product of Powers property?

Back

The general formula is a^m * a^n = a^(m+n), where 'a' is the base and 'm' and 'n' are the exponents.

Front

Can the Product of Powers property be applied to variables?

Back

Yes, the Product of Powers property can be applied to variables as long as the bases are the same.

Front

What happens when you multiply powers with different bases?

Back

When multiplying powers with different bases, you cannot combine the exponents. For example, a^m * b^n remains as is.

Front

How do you express the Product of Powers property in words?

Back

The Product of Powers property states that when multiplying two powers with the same base, you add the exponents.