Choose the correct simplification of the expression (3x)⁴.
81x⁴, 12x⁵, 81x⁵, 12x⁴

Solution:

The expression (3x)⁴ can be simplified as follows:

= (3x)⁴

= (3)⁴(x)⁴

= (3)(3)(3)(3)(x)(x)(x)(x)

= (9)(9)x⁴

= 81x⁴

Another example of a similar kind of problem can be: Choose the correct simplification of the expression (2x)⁶

(2x)⁶

= (2)⁶(x)⁶

= (2)(2)(2)(2)(2)(2)x⁶

= 64x⁶

Choose the correct simplification of the expression (3x)⁴.

Summary:

The correct simplification of the expression (3x)⁴ is 81x⁴.