Simplify (27x6)2/3

Solution:

We have (27x⁶)^2/3

we can write it as (3³ x⁶)^2/3

= 3^{3 × 2/3}  x ^{6 × 2/3}                             {(ab)^m = a^mb^m}

= 3² x⁴ 

= 9x⁴

Similar Questions

Question 1: Simplify: 7 – 3(x – 1)

Solution:

Here we have

7 – 3(x – 1)

= 7 – 3x +3

= 10 – 3x

= -3x + 10

Question 2:  Divide and simplify: (21x³ – 7)/(3x – 1).

Solution:

(21x³ – 7)/(3x – 1)

= [7 (3x³ – 1 )] / (3x-1)

= [ 7 {(3x)³ – (1)³ ] / (3x-1)

= [7 (3x-1)(9x² +1 + 3x)] / (3x-1) { a³ – b³ = (a – b)(a² + ab + b²) }

= 7 (9x² +1 + 3x)

= 63x² + 7 + 21x

= 63x² + 21x + 7

Question 3: Simplify for n: n + (n + 1) + (n + 2) = 87

Solution:

We have n + (n + 1) + (n + 2) = 87

n + n + 1 + n + 2 = 87 

3n + 3 = 87

3n = 87 – 3

3n = 84 

n = 84/3

n = 28

So the value of n is 28

Question 4: Solve for the value of t : 31 + t = 4 (t – 3) + 22

Solution:

We have 31 + t = 4 (t – 3) +22

31 + t = 4 (t – 3) + 22

31 + t =  4t – 12 + 22

31 + t =  4t + 10

31 – 10 = 4t – t 

21 = 3t

t  = 21/3

t = 7

So the value of t is 7

The basic concept of algebra taught us how to express an unknown value using letters such as x, y, z, etc.  These letters are termed here as variables. This expression can be a combination of both variables and constants.  Any value that is placed before and multiplied by a variable is termed a coefficient. An idea of expressing numbers using letters or alphabets without specifying their actual values is termed an algebraic expression.