EVALUTING NUMERIC EXPRESSIONS INVOLVING RATIONAL EXPONENTS

To evaluate numeric numeric values with rational exponents, we follow the steps given below.

Step 1 :

Express the base in exponential form.

Step 2 :

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

Step 3 :

Do possible simplification.

Evaluate the following :

Example 1 :

811/2

Solution :

= 811/2

Base = 81 and exponent = 1/2

81 = 92

811/2 = (92)1/2

= 9(2 x 1/2)

811/2 = 9

Example 2 :

163/2

Solution :

= 163/2

Base = 16, exponent = 3/2

16 = 42

= 4(2 x 3/2)

= 43

163/2 = 64

Example 3 :

100003/4

Solution :

= 100003/4

Base = 10000 and exponent = 3/4

10000 = 104

= 10(4 x 3/4)

= 103

= 1000

Example 4 :

642/3

Solution :

= 642/3

Base = 64 and exponent = 2/3

64 = 43

= 4(3 x 2/3)

= 42

= 16

Example 5 :

272/3

Solution :

= 272/3

Base = 27 and exponent = 2/3

27 = 33

= 3(3 x 2/3)

= 32

= 9

Example 6 :

81-3/2

Solution :

81-3/2

Base = 81 and exponent = -3/2

81 = 92

= 9 2 x (-3/2)

= 9-3

= 1/93

= 1/729

Example 7 :

If c2/5 = 4, then c = ?

Solution :

c2/5 = 4

Raising power 5 on both sides.

(c2/5)5 = 45

c(2/5) x 5 = 45

c= 45

Take square roots on both sides.

c = 45

c = 4x44

c = 16√(2x2)

c = 16(2)

c = 32

Example 8 :

274/x = 81, x = ?

Solution :

274/x = 81

Try to express the bases 27 and 81 as a multiple of 3.

33 = 27 and 34 = 81

33(4/x) = 34

312/x = 34

Since the bases are equal, we can equate the powers.

12/x = 4

Take reciprocal on both sides.

x/12 = 1/4

Multiply 12 on both sides.

x = 12/4

x = 3

Example 9 :

201/2 ⋅ 201/2

Solution :

201/2 ⋅ 201/2

Using the property a⋅ an = am+n

= 201/2 ⋅ 201/2

= 20(1/2 + 1/2)

= 20

Example 10 :

51/3 ⋅ 251/3

Solution :

= 51/3 ⋅ 251/3

25 = 52

= 51/3 ⋅ (52)1/3

= 51/3 ⋅ 52/3

= 5(1+2)/3

= 53/3

= 5

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