# Simplify Powers With Fractional Bases Worksheet

## 8 problems

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 fractions" target="_blank" class="backlink">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.

Exponents
7.NS.A.2.C

## Teaching the Simplifying Powers With Fraction Bases Easily

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.  &n...

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