EXPONENTS WITH DECIMAL AND FRACTIONAL BASES WORKSHEET

About "Exponents with decimal and fractional bases worksheet"

Exponents with decimal and fractional bases worksheet:

Here we are going to see some examples problems on exponents with decimal and fractional bases.

How to evaluate exponents with decimal bases ?

To evaluate an expression with decimal bases, first we have to convert the decimal number as integer.
For that we have to multiply it by 10, 100, 1000,etc.
Once we convert the decimal as fraction, we can distribute the power for both numerator and denominator separately.

How to evaluate exponents with fractional bases ?

To evaluate exponents with fractional bases, we have to distribute the power for numerator and denominator separately.

Let us see some practice problems based on the above concepts.

(1) Solve the following expressions

(2/5)³

(2) Solve the following expressions

(0.2)³

(3) Solve the following expressions

(0.29)²

(4) Solve the following expressions

(0.01)³

(5) Solve the following expressions

(5/2)³

Exponents with decimal and fractional bases worksheet -Solution

Question 1 :

Solve the following expressions

(2/5)³

Solution :

Since the given question is a fraction, we have to distribute the powers.

= 2³/3³

2³ means we have to multiply the base (2) three times like wise 3³ means we have to multiply 3 three times.

= (2 x 2 x 2)/(3 x 3 x 3)

= 8/27

Hence the answer is 8/27.

Question 2 :

Solve the following expressions

(0.2)³

Solution :

Since the given question is in the form of decimal, we have to convert this into a fraction, then we can easily evaluate the exponent.

In order to remove the decimal point, we have to multiply and divide both numerator and denominator by 10.

0.2 = 0.2 x (10/10) = 2/10

= (2/10)³

= 2³/10³

= (2 x 2 x 2)/(10 x 10 x 10)

= 8/1000

Since we have three zeroes in the denominator, we have to move the decimal point three digits to the left.

Hence the answer is 0.008.

Question 3 :

Solve the following expressions

(0.29)²

Solution :

Since the given question is in the form of decimal, we have to convert this into a fraction, then we can easily evaluate the exponent.

In order to remove the decimal point, we have to multiply and divide both numerator and denominator by 100.

0.29 = 0.29 x (100/100) = 29/100

= (29/100)²

= (29 x 29)/(100 x 100)

= 841/10000

Since we have four zeroes in the denominator, we have to move the decimal point four digits to the left.

Hence the answer is 0.0841.

Question 4 :

Solve the following expressions

(0.01)³

Solution :

Since the given question is in the form of decimal, we have to convert this into a fraction, then we can easily evaluate the exponent.

In order to remove the decimal point, we have to multiply and divide both numerator and denominator by 100.

0.01 = 0.01 x (100/100) = 1/100

= (1/100)³

= (1 x 1 x 1)/(100 x 100 x 100)

= 1/1000000

Since we have four zeroes in the denominator, we have to move the decimal point six digits to the left.

Hence the answer is 0.000001

Question 5 :

Solve the following expressions

(5/2)³

Solution :

Since the given question is a fraction, we have to distribute the powers.

= 5³/2³

= (5 x 5 x 5)/(2 x 2 x 2)

= 125/8

Hence the answer is 125/8.

After having gone through the stuff given above, we hope that the students would have understood "Exponents with decimal and fractional bases worksheet".

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