• To simplify an expression with powers, first write the numbers with the same base if possible, then apply the laws of exponents, and finally find the value.
• For example, 43 = (22)3 = 26 = 64, because 4 = 22.

Powers of algebraic expressions

• The same laws apply to letters.
• For example, x2 × x3 = x5, and (2x)3 = 23 × x3 = 8x3.
• When dividing, we subtract the exponents: 12y6 ÷ 3y2 = 4y4.
• Another example: (2x2)3 ÷ 4x4 = 8x6 ÷ 4x4 = 2x2.
• To check any result, substitute a numerical value: when x = 2, x2 × x3 = 4 × 8 = 32 = 25.
• To compare powers, we evaluate them 25 = 32 and 52 = 25, so 25 is greater than 52, even though the base 5 is greater than the base 2.

• Students sometimes think that (a^m)ⁿ equals a^m + aⁿ, but the exponents multiply. For example, (2²)³ = 2⁶ = 64, while 2² + 2³ = 12.