CONVERTING RATIONAL EXPONENTS TO RADICALS

Conversion Between Exponential and Radical

Exponential formRadical formx12xx133xx23x213=3x2x25x215=5x2

Write each expression in radical form.

Problem 1 :

x12

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= x1 · 12 Power 12 can used as square root.= x

Problem 2 :

x75

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= x7 · 15 Power 15 can used as fifth root.= 5x7

Problem 3 :

(5x)74

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= 5x7 · 14 Power 14 can used as fourth root.= 4(5x)7= 478125x7

Problem 4 :

(5a)34

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= 5a3 · 14 Power 14 can used as square root.= 4(5a)3= 4125a3

Problem 5 :

(6n)12

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= 6n1 · 12 Power 12 can used as square root.= 6n

Problem 6 :

5x214

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= 5x21 · 14 Power 14 can used as fourth root.= 45x2

Problem 7 :

(6x)52

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= 6x5 · 12 Power 12 can used as square root.= (6x)5= 7776x5

Problem 8 :

n56

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= n5 · 16 Power 16 can used as sixth root.= 6n5

Problem 9 :

(6r)43

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= 6r4 · 13 Power 13 can used as cube root.= 3(6r)4= 31296r4

Problem 10 :

(5v)13

Solution :

We can write the fractional power as product of integer and fraction.

So, we get

= 5v1 · 13 Power 13 can used as cube root.= 35v

Recent Articles

  1. Factoring Exponential Expression Using Algebraic Identities Worksheet

    Mar 14, 24 10:44 PM

    Factoring Exponential Expression Using Algebraic Identities Worksheet

    Read More

  2. Positive and Negative Numbers Connecting in Real Life Worksheet

    Mar 14, 24 10:12 AM

    Positive and Negative Numbers Connecting in Real Life Worksheet

    Read More

  3. Positive and Negative Numbers Connecting in Real Life

    Mar 14, 24 09:52 AM

    Positive and Negative Numbers Connecting in Real Life

    Read More