Laws of Exponents: Power of a Power

Front

What is the Power of a Power Rule in exponents?

Back

When raising a power to another power, you multiply the exponents. For example, (a^m)^n = a^(m*n).

Front

Simplify (x^2)^5.

Back

x^(2*5) = x^10.

Front

What happens to the exponents when multiplying powers with the same base?

Back

You add the exponents. For example, a^m * a^n = a^(m+n).

Front

Simplify (3y^4)^2.

Back

3^2 * (y^4)^2 = 9y^8.

Front

What is the result of (ab)^3?

Back

a^3 * b^3.

Front

Simplify (2x^3)^4.

Back

2^4 * (x^3)^4 = 16x^{12}.

Front

What is the result of (m^5n^3)^2?

Back

m^(5*2) * n^(3*2) = m^{10}n^6.

Front

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

Back

2^3 * (x^2)^3 * (y^3)^3 = 8x^6y^9.

Front

What is the result of (x^2y^3)(x^4y^2)?

Back

x^(2+4) * y^(3+2) = x^6y^5.

Front

Simplify (5a^2b^3)^2.

Back

5^2 * (a^2)^2 * (b^3)^2 = 25a^4b^6.