I'm new here in highschool and I don't know which is correct... (x^5)(x^5) = "x^10" or "2x^5"?

Answer 1

(x^5)(x^5) =x^(5+5) = x^10

add the exponents when multiplying variables or numbers with the same base

(2^5)(2^5) =2^(5+5) = 2^10 = 32(32) = 1024

add the coefficients when adding (an implicit coefficient of 1)

x^5 + x^5 =(1)x^5 + (1)x^5 + (1+1)x^5 = 2x^5

2^5 +2^5 = 32+32 = 64

2^5 +2^5 = 2(2^5) = 2(32) = 64

if you're not sure what to do, try a specific example with small simple integers

(2^2)(2^2) = 4(4) = 16

(2^2)(2^2) = 2^(2+2) = 2^4 = 16

(2^2)+(2^2) = 4+4=8

(2^2)+(2^2) = 2(2^2) = 2(4) = 8