Exponents: Power of a Product

Front

What is the power of a product rule in exponents?

Back

The power of a product rule states that (ab)^n = a^n * b^n, meaning you can distribute the exponent to each factor in the product.

Front

Simplify: (3xy)^4

Back

81x^4y^4

Front

What happens when you raise a power to a power?

Back

When you raise a power to a power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

Simplify: (x^2y^3)^3

Back

x^6y^9

Front

What is the result of (a^m)(a^n)?

Back

The result is a^(m+n), which means you add the exponents when multiplying like bases.

Front

Simplify: (2x^3)^2

Back

4x^6

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

Simplify: (x^5)^2

Back

x^{10}

Front

What is the negative exponent rule?

Back

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

Front

Simplify: (2a^3b^2)^2

Back

4a^6b^4