Example 1

Simplify the powers.

a) [[$ (2 \cdot 3)^3 = 2^3 \cdot 3^3 = 8 \cdot 27 = 216 $]]​

b) [[$ (2x)^3 = 2^3 \cdot x^3 = 8x^3 $]]​

c) [[$ (5a^3b)^2 = 5^2 \cdot a^{3\cdot2} \cdot b^2 = 25a^6b^2 $]]​

d) [[$ \dfrac{(2xy)^3}{2x^2} = \dfrac{2^3x^3y^3}{2x^2} = 2^{3-1} x^{3-2} y^3 = 2^2 xy^3 = 4xy^3 $]]​

Example 2

Express as one power.

a) [[$ 2^3 \cdot 4^3 = (2\cdot 4)^3 = 8^3 $]]​

b) [[$ 16x^2y^2 = 4^2x^2y^2 = (4xy)^2 $]]​