Question

The expression -4n^6x2n^2 is equivalent to cn^x, what is the value of x?

a) 4
b) 6
c) 8
d) 10

Answer 1

When combining the like terms involving the variable 'n' by multiplying coefficients and adding exponents, we find the equivalent expression to be -8n^8, which shows that the value of 'x' is 8.

Step-by-step explanation:

The expression given is -4n^6 \times 2n^2. To find the equivalent expression of the form cn^x, we need to combine the like terms involving the variable n. Multiplying the coefficients gives us -8, and adding the exponents of the variable n (since this is a multiplication of like bases) gives us n^8. Therefore, the equivalent expression is -8n^8, which means the value of x is 8.

To exemplify, the multiplication of powers with the same base can use the rule n^a \times n^b = n^(a+b). Thus, in this question:
-4n^6 \times 2n^2 = (-4 \times 2)(n^6 \times n^2) = -8n^(6+2) = -8n^8