幂的运算性质是指同底数的幂相乘(除),幂的乘方,积的幂,这些性质均可以逆用,逆用这些性质解整式乘(除)问题,往往能开启解题思路.1.指数相加的幂写成同底数幂的积,即a~(m+n)=a~ma~n.例1已知2~(x+1)=m,用含m的式子表示2~x.解因为2~(x+1)=2~x·2,所以2~x·2=m,2~x=m/2.2.指数相乘的幂写成幂的乘方.即a~(mn)=(a~m)~n.例2已知3~(2x)=81,求x的值.解因为3~(2x)=(3~2)~x=9~x=81=9~2,所以x=2.3.相同指数幂的积写成积的幂.即a~mb~m=(ab)~m.例3计算2~2×4~2×(3/8)~2.解2~2×4~2×(3/8)~2=(2×4×3/8)~2=9. Exponentiation of power means multiplying (dividing) the power of the same base, the power of the power, the power of the product, and these properties can all be reversed. Using these properties to solve integer multiplication problems can often open the way to solve problems .1. The exponential sum power is written as the product of the same base powers, ie a ~ (m + n) = a ~ ma ~ n. Example 1 Known 2 ~ (x + 1) = m, 2 x x 2 = m, 2 x = m / 2.2 The exponent multiplied by the power is written as the power of the exponent, that is, (mn) = (a ~ m) ~ n Example 3 Known 3 to (2x) = 81, the value of x is obtained. The solution is that 3 to 2x = 3 to 2 ~ x = 9 to x = 81 = 9 ~ 2, so x = 2.3. The product of the same exponential power is written as the power of the product, ie a ~ mb ~ m = (ab) ~ m. Example 3 Calculate 2 ~ 2 × 4 ~ 2 × ) ~ 2. Solutions 2 ~ 2 × 4 ~ 2 × (3/8) ~ 2 = (2 × 4 × 3/8) ~ 2 = 9.