CONVERTING EXPONENTIAL FORM TO RADICAL FORM

Write each expression in radical form :

Problem 1 :

m3/5

Solution :

= m3/5

We can write the fractional power as product of integer and fraction. So, we get

= m⋅ (1/5)

Power 1/5 can be used as 5th root.

5m3

Problem 2 :

(10x)-3/4

Solution :

First let us write -3/4 as a product of integer and fraction.

(10x)-3/4  =  (10x)-3 ⋅ (1/4)

Changing power 1/4 as 4th root.

=  4(10x)-3

In order to change the negative exponent as positive exponent, we will flip the base.

=  4√1/(10x)3

= 1/4(10x)3

Problem 3 :

(7x)3/2

Solution :

= (7x)3/2

Writing the fractional power as a product of integer and fraction, we get

= (7x)3⋅ (1/2)

Power 1/2 can be written as square root.

= √(7x)3

Here 7x is repeated 3 times inside the square root.

Accordingly the rule in square root, if we see two same terms inside the square root, we can take one out of the radical.

= √(7x) (7x) (7x)

= 7x√(7x)

Problem 4 :

(6b)-4/3

Solution :

= (6b)-4/3

Writing the fractional power as a product of integer and fraction, we get

= (6b)-4⋅ (1/3)

1/3 can be written as cube root.

3(6b)-4

In order to change the negative exponent as positive exponent, we will flip the base.

3√1/(6b)4

Since it is cube root, we take one term out of the cube root for every three same terms.

3√1/(6b) ⋅ (6b) ⋅ (6b) ⋅ (6b)

= 1/(6b 3√6b)

Problem 5 :

82/3

Solution :

Method 1 :

= 82/3

= 8⋅ (1/3) 

Writing 1/3 as cube root.

382

3√64

3√(4 ⋅ 4 ⋅ 4)

= 4

Method 2 :

When we evaluate with just numerical values in the base, we will try to write the base in exponential form.

= 82/3

Writing 8 in exponential form, we get 8 = 23

= (23)2/3

When we have power raised to another power, we will multiply both the powers.

= 23 x (2/3)

= 22

= 4

Problem 6 :

100-3/2

Solution :

Method 1 :

= 100-3/2

100-3(1/2)

√(100)-3

= 1/√(100)3

= 1/100√100

= 1/100(10)

= 1/1000

Method 2 :

= 100-3/2

Writing 100 in exponential form, we get

100 = 102

= (10)2(-3/2)

= 10-3

= 1/103

= 1/1000

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