If x ≠ 0, what is the sum of 4∛x^10 +5x^3∛8x in simplest form?
Answer (2)
The simplified form of the expression 4 3 x 10 + 5 x 3 3 8 x is 14 x 3 3 x . This is achieved by simplifying each term individually and then combining the like terms. The answer reflects an understanding of cube roots and exponent manipulation.
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To find the sum of the expressions 4 3 x 10 + 5 x 3 3 8 x , we first simplify each term individually.
Simplifying 4 3 x 10 :
The cube root of x 10 can be expressed by rewriting the exponent: x 10 = ( x 3 ) 3 ⋅ x 1 .
Thus, 3 x 10 = x 3 3 x .
Therefore, 4 3 x 10 = 4 x 3 3 x .
Simplifying 5 x 3 3 8 x :
The cube root of 8 x can be broken down as 3 8 ⋅ 3 x , where 3 8 = 2 .
Therefore, 5 x 3 3 8 x = 5 x 3 ⋅ 2 ⋅ 3 x = 10 x 3 3 x .
Adding the two expressions together:
Now, adding both simplified terms gives us: 4 x 3 3 x + 10 x 3 3 x = ( 4 + 10 ) x 3 3 x = 14 x 3 3 x .
Therefore, the sum in simplest form is 14 x 3 3 x .
