In mathematics, Powers and exponents are ways to write extremely large or small numbers in a simple and easily readable format; especially when the numbers are in fraction format. Exponents with fractions in maths are expressions showing repeat multiplication of fractional numbers. Any fractional number having some powers such as (½ )2 is an exponential expression with a fractional base.
Consider (p/q)x a simple exponential expression having a fractional base.
As per the definition, an exponational expression means multiplying a number by itself multiple times.
For simplifying (p/q)x, we will have to multiply p/q by itself upto x times.
Example: if p/q is raised to power 6; we can write it a (p/q)6 and for simplifying it.
(p/q)6 = p/q * p/q * p/q * p/q * p/q * p/q
It can also be written as p6/q6.
So, the formula for simplifying a fractional base exponent is (p/q)x = px/qx .
For example: (2/3)2 = 22/32 = 4/9.
Fractional base having negative power:
If a fractional base (p/q)-x have negative power, it is reciprocated and the power is turned positive.
(p/q)-x will be written as 1 / (p/q)x = 1 / (ax/bx) = bx/ax.
For example: (3/2)-2 = 1 / (3/2)x = 1 / (32/22) = 22/32 = 4/9.
Multiplication of Fraction base:
1. Having same base but different powers
(p/q)x * (p/q)a = (p/q)x+a
Example: (1/3)3 * (1/3)2 = (1/3)3+2&...
