How to calculate the fractional power of a number?

How to calculate the fractional power of a number?

The score is indexed to a root
For example: 2 ^ 1.5 = 2 ^ (3 / 2) = 2 times root (2 ^ 3) = root 8 = 2 √ 2

What is the difference between the fractional power and the decimal power of a number? How to calculate it? For example, 4 ^ 0.75 = 2.828427125 But 4 ^ 3 / 4 = 16. What's going on?

4 ^ 0.75 = 4 ^ (3 / 4) = open 4 roots (4 ^ 3) = (4 ^ 3) ^ (1 / 4) = 2.828427125
4^3/4==(4^3)/4=16
See?

To the power of + 1?

The fifth power of (1 + I)
=(1+i)^4*(1+i)
=[(1+i)^2]^2*(1+i)
=[2i]^2*(1+i)
=-4(1+i)
=-4-4i

3 to the 14th power X (- 1 / 9) to the 5th power

The 14th power of 3 x the 5th power of (- 1 / 9)
=The 7th power of 9 x the 5th power of (- 1 / 9)
=The 5th power of 9? 2 × 9 x the 5th power of (- 1 / 9)
=The fifth power of 9 × [9x (- 1 / 9)]
=-81

How to calculate the fifth power of (x square + 1 / X to the third power)?

The fifth power of (x square + 1 / x) is x ^ 10 + 5 * x ^ 5 + 10 + 10 / x ^ 5 + 5 / x ^ 10 + 1 / x ^ 15

Calculate the 2012 power of (- 1) + (- 3) to the 2nd power ×| - 2 × 3 to the power of 1 | (- 4 to the 3rd power) / (- 2 to the 5th power) 5 to the 2nd power △ 8 × (- 2 / 5 to the 3rd power)

The 2012 power of (- 1) + (- 3) to the 2nd power ×| - 2 × 3 to the power of 1 - (- 4 to the 3rd power) / (- 2 to the 5th power)
=1+9×|-1/6|-（-64）÷（-32）
=1+3/2-2
=1/2
5 to the 2nd power △ 8 × (- 2 / 5 to the 3rd power)
=25÷8/125×（-8/125）
=-25

Calculate (1-1 / 2 squared) (1-1 / 2 to the third power) (1-1 / 2 to the ninth power) (1-1 / 2 to the tenth power)

The deformation is 10-1 / 2 squared - 1 / 2 cubic -The tenth power of 1 / 2 = 10-1 / 2 (1-1 / 2) ^ 9

Mathematical calculation: the first power of 3 + the second power of 3 + the third power of 3... + the n power of 3=

We know the following formula for the sum of the preceding numbers:
A1 (1-Q ^ n) / (1-Q) = (A1 an * q) / (1-Q) (q is the common ratio and Q ≠ 1)
A1 = 3, common ratio q = 3
3（1-3^n)/(1-3)=3(3^n-1)/2

Calculation: the M-1 power of a is multiplied by the cubic power of a-2a is multiplied by the fourth power of a-3a is multiplied by the M + 2 power of A calculation: The M-1 power of a is multiplied by the cubic power of a-2a is multiplied by the fourth power of a-3a is multiplied by the M + 2 power of A PS: the addition and subtraction index must be the same And explanation

=A to (M + 2) - 2a to (M + 4) - 3a to (M + 4)
=The (M + 2) power of a - the (M + 4) power of 5A

Calculate s = 1 + 2 + 2 quadratic + 2 cubic. 2 2013 power It is suggested that 2S = 2 + 2's quadratic power + 2's cubic power + 2's 2013 power + 2's 2014 power

I don't know why you want to prompt. But the 0 power of 2 is 1, so this is an equal ratio sequence with a common ratio of 2 and a cardinal number of 2
An = A1 × Q ^ (n-1). So s = 2 to the 2014 power