# USING PATTERNS OF INTEGER EXPONENTS

In this section, we are going to see, how to use the patterns of integer exponents to find the forth coming terms in the sequence of numbers.

The table below shows powers of 5, 4, and 3. Question 1 :

What pattern do you see in the powers of 5 ?

As the exponent decreases by 1, the value of the power is divided by 5.

Question 2 :

What pattern do you see in the powers of 4 ?

As the exponent decreases by 1, the value of the power is divided by 4.

Question 3 :

What pattern do you see in the powers of 3 ?

As the exponent decreases by 1, the value of the power is divided by 3.

Question 4 :

What are the values of 50 5-1 5-2 and 5-3 ?

From the table, we come to know the fact, as the exponent decreases by 1, the value of the power is divided by 5.

And also, from the table, we have 51 =  5.

Since 5 =  5, we get 50  =  5 ÷ 5  =  1.

Since 50 =  1, we get 5-1  =  1 ÷ 5  =  1/5.

Since 5-1  =  1/5, we get  5-2 =  (1/5) ÷ 5  =  1/25.

Since  5-2  =  1/25, we get 5-3  =  (1/25) ÷ 5  =  1/125. Question 5 :

What are the values of 40 4-1 4-2 and 4-3 ?

From the table, we come to know the fact, as the exponent decreases by 1, the value of the power is divided by 4.

And also, from the table, we have 41 =  5.

Since 4 =  4, we get 40  =  4 ÷ 4  =  1.

Since 40 =  1, we get 4-1  =  1 ÷ 4  =  1/4.

Since 4-1  =  1/4, we get 4-2  =  (1/4) ÷ 4  =  1/16.

Since  4-2  =  1/16, we get 4-3  =  (1/16) ÷ 4  =  1/64. Question 6 :

What are the values of 30 3-1 3² and 3³ ?

From the table, we come to know the fact, as the exponent decreases by 1, the value of the power is divided by 3.

And also, from the table, we have 31  =  3.

Since 31  =  3, we get 30  =  3 ÷ 3  =  1.

Since 30  =  1, we get 3-1  =  1 ÷ 3  =  1/3.

Since 3-1  =  1/3, we get  3-2  =  (1/3) ÷ 3  =  1/9.

Since  3-2  =  1/9, we get 3-3  =  (1/9) ÷ 3  =  1/27. ## Reflect

1.  Write a general rule for the value of a0, a ≠ 0 ?

a0  =  1

2.  Write a general rule for the value of a-n, where a ≠ 0 and n is an integer ?

a-n  =  1/an Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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