Are you worried about the solution of Exponential expressions? It is really not so difficult as you think. It may confuse you or irritate you when you experience solving them for the first time. But I assure you, It is going to be very interesting to learn how to get rid of exponents. Just stay with me.
I think it is very necessary to introduce you to the exponents to make a clear and lucid concept about exponents. Exponents/Indices are the repeated multiplication of a number. For example,
2^2 = 2.2, it is repeated multiplication of 2.
3^2 = 3.3, it is repeated multiplication of 3.
X^3 = X.X.X, it is repeated multiplication of X.
Y^4 = Y.Y.Y.Y, it is repeated multiplication of Y.
If 2 is the index of a number 3, it means number 3 will be multiplied with itself two times. Same as, if 4 is the index of a variable Y, it means Y will be multiplied with itself four times.
One more noticeable thing is, Commutative property does not exist in exponential expressions eg, 2^5 ≠ 5^2
How To Get Rid Of Exponents?
To learn, how to get rid of exponents, I shall introduce you to the Laws of Exponents.
How To Get Rid Of Zero Property Exponents?
Zero property is the funniest property in learning, how to get rid of exponents. If the index/exponent of a number is zero, it results in 1.
e.g. 2^0 = 1
3^0 = 1
X^0 = 1 (0^0 = 1)
Let us see another example
It does not matter what is the Base, when it gets ‘o’ index it becomes equal to 1.
How To Get Rid Of Negative Exponents?
Negative exponents mean that the Index of a Non zero number is negative. Usually, when students face a negative exponent they get worried and think about how to get rid of negative exponents. I am going to show you from a simple negative exponent to a complex negative exponent solution.
(1) For example; 2^-2 here, the base is 2, and the exponent is -2. We shall solve it according to the Negative property of Exponents. As we know that expression(2^-2) is in the numerator, We’ll simply move it to the Denominator to make the Exponent positive.
e.g. 1/2^2 which is equal to 1/4.
It means you get rid of negative exponents by changing its position in a fraction. Let us see some other examples to make the concept clear.
(3) Look at some other examples,
(4) Example: In the case of a complex expression, you’ll solve it in this way.
I hope these examples would have made your concept clear. Now you will find it easy, ‘how to get rid of negative exponents’.
How to Solve the Product Property of Exponents?
It is also very easy to solve such non zero numbers that have exponents and are multiplied with each other. According to the Lw of Product Property Exponents, when two bases are multiplied then their exponents are added. Let us look at some simple as well as complex examples to make a proper sense.
(1) Example: (Note; It is valid when bases are the same.)
If exponents are the same but bases are different then bases are multiplied and exponent remains the same. The complex form will be solved like this,
This is how to get rid of exponents in product property.
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How to Solve Quotient Property of Exponent?
When you multiply two exponents with the same base, you add the exponents and when you divide two exponents with the same base you subtract the exponents,
Simply, this is how to get rid of exponents in quotient in quotient form.
How to Solve Power of a Power Property Exponent?
When an exponential expression has power, then both the powers are multiplied to simplify the statement. Let us take a glimp of some examples.
This is how to get rid of exponents in the property power of the power.
How to Solve Power of a Product Property of Exponent?
If there is more than one term in parenthesis, with an exponent outside the parenthesis, then the exponent is multiplied to every term in the parenthesis. Here, are some examples to make sense clear.
the power is distributed to every term in the parenthesis.
I hope you are enjoying learning, how to get rid of exponents with respect to the different properties of exponents.
How to Solve the power of Quotient Property of Exponents?
To solve the Power of quotient property, Power is distributed to every term in the parenthesis. See some examples for clarification.
That’s the simplest way to learn how to get rid of exponents when the expression is the power of a quotient.
Now I am going to introduce you to some worrying form of exponential expressions. I recommend you, students, just go through the deep guidance and try once before you quit.
How to Get Rid of Exponents in Algebra?
When you move from the solution of simple exponential expressions towards the solutions of Algebric exponential expressions, you may get confused. But don’t worry students, the main purpose of this article is to root out this confusion and make the exponent’s solution easy to you. YOu will cover here the different type of Algebraic equations which confuse the most.
Negative Exponents Algebraic Equation
It is easier to learn than you think, how to get rid of exponents with a negative sign in the equation.
Another example is
Look at another type
Another type is
A fractional case is solved in this way
This is how to get rid of exponents in fractions.
Getting an expert in mathematics is all about practice. The more you practice the more you will find it easy and interesting. However, if you think you need more practice you should watch this video.
Final words :
I hope you will find this article much helpful for you even if you are totally unfamiliar with the exponents. After reading this explanation you will know how to get rid of exponents. You will feel much confident to solve the simple as well as complex exponential expressions. Make learning math joyous