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Power

Power(a, b)


a ^ b

represents a raised to the power of b.

Note: Power has the Listable attribute and Power(x,y,z) is grouped as x^(y^z)

You can’t do matrix calculations with the ^operator:

>> {{2,1},{1,1}} ^ 2

is computed as:

{{2^2,1^2},{1^2,1^2}}

Use Inverse({{2,1},{1,1}}) or MatrixPower({{2,1},{1,1}},2) to calculate matrix inverses and powers.

Don’t confuse the ^ operator with the ^^ operator, which can be used for integer number bases other than 10. Here’s an example for a hexadecimal number:

>> 16^^abcdefff
2882400255

See

Examples

>> 4 ^ (1/2)
2


>> 4 ^ (1/3)
4^(1/3)


>> 3^123
48519278097689642681155855396759336072749841943521979872827


>> (y ^ 2) ^ (1/2)
Sqrt(y^2)


>> (y ^ 2) ^ 3
y^6

Use a decimal point to force numeric evaluation:

>> 4.0 ^ (1/3)
1.5874010519681994

Power has default value 1 for its second argument:

>> a /. x_ ^ n_. :> {x, n}
{a,1}

Power can be used with complex numbers:

>> (1.5 + 1.0*I) ^ 3.5
-3.682940057821917+I*6.951392664028508


>> (1.5 + 1.0*I) ^ (3.5 + 1.5*I)
-3.1918162904562815+I*0.6456585094161581

Infinite expression 0^(negative number)

>> 1/0
ComplexInfinity


>> 0 ^ -2
ComplexInfinity


>> 0 ^ (-1/2)
ComplexInfinity


>> 0 ^ -Pi
ComplexInfinity

Indeterminate expression 0 ^ (complex number) encountered.

>> 0 ^ (2*I*E)
Indeterminate


>> 0 ^ - (Pi + 2*E*I)
ComplexInfinity

Indeterminate expression 0 ^ 0 encountered.

>> 0 ^ 0
Indeterminate


>> Sqrt(-3+2.*I)
0.5502505227003375+I*1.8173540210239707


>> Sqrt(-3+2*I)
Sqrt(-3+I*2)


>> (3/2+1/2I)^2
2+I*3/2


>> I ^ I
I^I


>> 2 ^ 2.0
4.0


>> Pi ^ 4.
97.40909103400242


>> a ^ b
a^b


>> Power(x,y,z)
Power(x,Power(y,z))

BaseForm, MatrixPower, Times

Implementation status

  • ✅ - full supported

Github