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 = (1/3)5 = 1/243.
2. Having same power but different base:
(p/3q)x * (m/n)x = ((p/q)(m/n))x
Example: (1/3)2 * (1/2)2 = ((1/3) * (1/2))2 = (1/6)2 = 1/36.
Practicing fractional exponent worksheets will help students to easily understand various concepts of exponents applied on fractional numbers.
Additionally, they will be able to solve multiple fractional exponents problems by applying the concepts.
Download these class 8 simplifying powers with fractional bases worksheets PDF for your students. You can also try our Simplify Powers With Fractional Bases Problems and Simplify Powers With Fractional Bases Quiz as well for a better understanding of the concepts.
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&...
