CONVERTING RADICALS TO RATIONAL EXPONENTS

Converting Radicals to Rational Exponents

Write each expression in exponential form.

Problem 1 :

33n

Solution :

Cube root can be written as power 1/3.

= (3n)13= 313 ·n13

Problem 2 :

32a

Solution :

Cube root can be written as power 1/3.

= (2a)13= 213 ·a13

Problem 3 :

4b5

Solution :

Fourth root can be written as power 1/4.

4b5 = b1454b5 = b54

Problem 4 :

6n2

Solution :

Sixth root can be written as power 1/6.

= n216= (n)2 × 16= (n)13

Problem 5 :

36k2

Solution :

Cube root can be written as power 1/3.

= 6k132= (6k)13 × 2= (6k)23= 623 · k23

Problem 6 :

2p5

Solution :

Square root can be written as power 1/2.

= 2p125= (2p)12 × 5= (2p)52= 252 · p52

Problem 7 :

53n7

Solution :

Fifth root can be written as power 1/5.

= 3n157= (3n)15 × 7= (3n)75= 375 · n75

Problem 8 :

610n2

Solution :

Sixth root can be written as power 1/6.

= 10n216= (10n)2 × 16= (10n)13= 1013 · n13

Problem 9 :

5x8

Fifth root can be written as power 1/5.

= x158= (x)15 × 8= (x)85

Problem 10 :

33x2

Solution :

Cube root can be written as power 1/3.

= 3x132= (3x)13 × 2= (3x)23= 323 · x23

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