NEGATIVE EXPONENT RULES

About "Negative exponent rules"

On the webpage "Negative exponent rules",we are going to see how to convert a negative exponent as positive exponent and also we are going to see how to perform simplification using negative exponents.

Exponents with negative powers

Whenever we have a negative number as exponent and we need to make it as positive,we have to flip the base that is write the reciprocal of the base and we can change the negative exponent as positive exponent.

Let us see some examples to understand this concept.

Integer with negative exponent:

Fractions with negative exponents

Negative numbers with positive exponents

In the below example we are going to how to evaluate the value of negative numbers with positive exponent.

Evaluate (-3) 

          = (-3) x (-3) x (-3) x (-3) x (-3) 

          = -343

The same problem can be done in another simple way.

Decimal numbers with negative exponents

Whenever we have decimal number in the base with negative exponent and we need to evaluate that,first we try to change the decimal as integer by multiplying 10s,100s and so on.

In the below example we are going to how to evaluate the value of decimal numbers with negative exponent.

Evaluate 0.4²

In step 1 we are going to convert 0.4 as integer for that we have to multiply and divide it by 10.

After multiplication we get 4/10.To change the negative exponent as positive we are going to flip the fraction and change the negative exponent as positive.

If it is possible we can simplify and distributing the power we get

So answer is 6.25

More example problems using negative exponent rules

Simplify using negative exponent rules:

Problem 1:

Simplify (3x)¹

Solution:

          = (3x)¹

We have negative power and we want to make it as positive. To make it as positive we need to write its reciprocal.The reciprocal of 3x is 1/3x

          = (1/3x)¹

by distributing the power we get

         = 1¹/(3x)¹

        = 1/3x

Let us see the next example problem of the topic "negative exponent rules".

Problem 2:

Simplify 2pr

Solution:

          = 2pr

We have negative power for r only.So we have to write the reciprocal of r and we can change the negative power as positive.

          = 2p(1/r)

          = 2p(1/r⁵)

          = 2p/r⁵

Let us see the next example problem of the topic "negative exponent rules".

Problem 3:

Simplify -xy¹/9z²

Solution:

          = -xy¹/9z²

We have negative power for y and z.So we have to write the reciprocal of y and z and we can change the negative power as positive.

          = -(x/9) (1/y)¹ (1/z)²

          = -x/9 y z²

Problem 4:

Simplify  (5x/3yz)³

Solution:

          =  (5x/3yz)³

We have negative power for the whole fraction.To make it as positive exponent we have to flip the fraction.

          =  (3yz/5x)³

          =  3³y³z³/5³

        = 27y³z³/125

Problem 5:

Simplify  (52 x⁶/13x⁷)

Solution:

          =  (52 x⁶/13x⁷)

We have negative power for the x term which is in the denominator.To make it as positive we are going to write it in numerator.

           =  (52 xx/13)

           =  4 x

           =  4 x¹³

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