Question

Find the missing exponent. Set up an equation and solve. : x^4·x^n = x^5

N = missing exponent.

Please explain so I can understand.

Answer 1

remember
(x^m)(x^n)=x^(m+n)
and
if a^m=a^n, where a=a then n=m


(x^4)(x^n)=x^5
(x^4)(x^n)=x^(4+n)
x^(4+n)=x^5
therefor
4+n=5
minus 4
n=1

Answer 2

when a polynomial is composed of product or quotient of terms, the terms with similar bases have exponents equal to the sum or difference of the exponents. in this case, x^4·x^n = x^5. since all have similar bases, n should be 1 since 4 + 1 = 5