# SIMPLIFY EXPRESSIONS INVOLVING RATIONAL EXPONENTS

## About "Simplify expressions involving rational exponents"

Simplify expressions involving rational exponents :

Here we are going to see some practice questions on simplifying expressions involving rational exponents.

Rule 1 :

If we have same base for two or more terms which are multiplying , we have to write only one base and add the powers

am x an  =  a(m+n)

Rule 2 :

If we have same base for two or more terms which are dividing, we have to write only one base and subtract the powers

am / an  =  a(m-n)

Rule 3 :

If we want to change the negative power as positive, we have to take its reciprocal of the base and change the sign.

a-m =  1/am

(a/b)-m  =  (b/a)m

Let us look into some example problems based on the above concept.

## Simplify expressions involving rational exponents - Examples

Example 1 :

Simplify the following expression

Solution :

=  (3x-1/2 ⋅ 3x1/2 ⋅ y-1/3) / 3y-7/4

=  9x(-1/2) + (1/2) ⋅ y(-1/3) + (7/4)/ 3

=  (9x0 ⋅ y(-4+21)/12)/3

=  (9(1) ⋅ y17/12)/3

=  3y17/12

Step 1 :

We have to combine the x and y terms separately.

3x-1/2 ⋅ 3x1/2  =   9x(-1/2) + (1/2)

Since we bring the y term from denominator to numerator, we have changed the original sign from negative to positive.

y-1/3 y-7/4  =   y(-1/3) + (7/4)

Step 2 :

By combining the x terms, we get x0

For combining the y terms, we need to take L.C.M. So we get y17/12

Step 3 :

Hence the answer is  3y17/12

Example 2 :

Simplify the following expression

Solution :

=  3y1/4 /( 4x-2/3 ⋅ y3/2 3y1/2)

=  3y1/4 / (12 x-2/3 ⋅ y3/2 y1/2)

=  y1/4 / (4 x-2/3 ⋅ y(3/2) + (1/2)

=  y1/4 / (4 x-2/3 ⋅ y(3+1)/2)

=  y1/4 / (4 x-2/3 ⋅ y2)

=  x2/3/ (4 ⋅ y(-1/4) +2)

=  x2/3/ (4 ⋅ y(-1 + 8)/4)

=  x2/3/ (4 ⋅ y7/4)

Step 1 :

In the denominator, we multiply 4 and 3.

So we get 12 x-2/3 ⋅ y3/2 y1/2

In the denominator, we get y terms.So we get

y(3/2) + (1/2)  =  y2

Step 2 :

Hence the answer is  x2/3/ (4 ⋅ y7/4)

Example 3 :

Simplify the following expression

Solution :

To simplify the above expression, we have to use exponent rules.

Step 1 :

Since we have same bases for the above terms, we have to put only one base and add the powers.

Step 2 :

By considering the above fractions 2/3 and 7/3, we have same denominators for both fractions. So we dont have to take L.C.M

Step 3 :

Hence the simplified answer is y³

Example 4 :

Simplify and write the answer in positive exponents

Solution :

To simplify the above expression, we have to use exponent rules.

Step 1 :

Since we have same bases for the above terms, we have to put only one base and add the powers.

Step 2 :

By considering the above fractions 3/5 and 7/5, we have same denominators for both fractions. So we dont have to take L.C.M

Step 3 :

Hence the simplified answer is a²

Example 5 :

Simplify and write the answer in positive exponents

Solution :

To simplify the above expression, we have to use exponent rules.

Step 1 :

Here we have common power for both terms, so we have to distribute the power 1/2.

Step 2 :

Whenever we have power raised to another power, we have to multiply both powers.

Step 3 :

By simplifying 4 and 2, we get x²

Hence the simplified answer is x² y^(1/2)

Example 6 :

Simplify and write the answer in positive exponents

Solution :

To simplify the above expression, we have to use exponent rules.

Step 1 :

Here we have common power for both terms, so we have to distribute the power 2.

Step 2 :

Whenever we have power raised to another power, we have to multiply both powers.

Step 3 :

By simplifying 2 and 2, we get a

Hence the simplified answer is a b^(2/3)

Example 7 :

Simplify and write the answer in positive exponents

Solution :

To simplify the above expression, we have to use exponent rules.

Step 1 :

In the first step we have multiplied the numbers.

Step 2 :

Now we have to multiply a^1/2 and a. Since both are having same base, we have to put only one base and add the powers.

Step 3 :

By adding a^1/2 with a^1, we get a^3/2.

Hence the simplified answer is 6 a^(3/2)

After having gone through the stuff given above, we hope that the students would have understood "Simplify expressions involving rational exponents".

Apart from the stuff given above, if you want to know more about "Simplifying expressions with rational exponents worksheet", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6