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Introduction to Exponents

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What are Exponents?


exponents1
An exponent is the continued product of a number multiplied with itself a number of times. It can be written as the number raised to the power of a natural number, equal to the number of times the number is multiplied with itself.



exponents2For example: 8 × 8 can be written as 82 and it is read as 8 raised to the power 2 or second power of 8.

In 82, we call 8 as the base and 2 as the exponent or power.

Types of Exponents

Each type is discussed as follows:


Positive Exponents

Powers with positive integer exponents may be defined by the initial condition a1 = a and the recurrence relation an+1 = a•an

For example: 35, here as we know that 3 is the base and 5 is the exponent which is positive.

Try this:
1. If 25 = 32, then what would be 26 =?
(Answer: 64)

Negative Exponents

exponents3A negative exponent is defined as the reciprocal of that power with a positive exponent.
a−n is the reciprocal of an.

For example: 2-3 =

Try these questions now:

1. Express (2)-4 with a positive exponent.

2. What is the value of 4-2 ?


Fractional Exponents

A fractional exponent is defined as an exponent of the form 1/n, means to take the nth root instead of multiplying or dividing. For example, 41/3 is the 3rd root (cube root) of 4.

For example: What is 91/2?

91/2 is the square root of 9 which is 3.
∴ 91/2 = 3
Try these questions now:

1. Evaluate: 161/4
(Answer: 2)
2. Evaluate: 1281/7
(Answer: 2)

Zero Exponents

For any number (a) not equal to 0, a0=1 or any non-zero number raised to the power zero is equal to 1.

For example: 20 = 1

Try these questions now:

1. What is 1000?
(Answer: 1)
2. Evaluate: (200)0 + (100)0
(Answer: 2)
   

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