Python | sympy.powsimp() method

With the help of sympy.powsimp() method, we can simplify mathematical expressions using laws of indices involving powers.

Properties :
1) x**a*x**b = x**(a+b)
2) x**a*y**a = (xy)**a

Syntax: powsimp(expression)

Parameters:
expression – It is the mathematical expression which needs to be simplified.

Returns: Returns a simplified mathematical expression corresponding to the input expression.

Example #1:
In this example we can see that by using sympy.powsimp() method, we can simplify any mathematical expression using laws of indices involving powers.

# import sympy
from sympy import *

x, a, b = symbols('x a b')
expr = x**a * x**b

print("Before Simplification : {}".format(expr))

# Use sympy.powsimp() method
smpl = powsimp(expr)

print("After Simplification : {}".format(smpl))

Output:

Before Simplification : x**a*x**b
After Simplification : x**(a + b)

Example #2:

# import sympy
from sympy import *

x, a, b = symbols('x a b')
expr = ((x**(2 * a + b))*(x**(-a + b)))

print("Before Simplification : {}".format(expr))

# Use sympy.powsimp() method
smpl = powsimp(expr)

print("After Simplification : {}".format(smpl))

Output:

Before Simplification : x**(-a + b)*x**(2*a + b)
After Simplification : x**(a + 2*b)