Answer:
m=5
Step-by-step explanation:
Given:
([(x^m) (x^2)]^3) ([k^3)^5]= (x^21)(k^15)
we can simplify this equation by understanding what operation that was applied to the x and k variables
we can pridect that they were using the multiplication method of exponents by distribution as follows:
if we look at x^21 at the right side of the equation then we shold have the same nuber of x multiples such that:
21= (3)(7) but if we look at the right hand side we have some missing information but we can still use the multiplication of the exponent and subtract it from the right hand side as follows:
first distribute 3 for both x's in the left hand side:
(x^m)^3= x^(3)(m)
and
(x^2)^3= x^(2)(3)
⇒will give us:
(x^3m)(x^6)=(x^21)
let us now check by ignoring the x's and use the exponents in the form of an equation:
(3m)+(6)=21
move 6 to the right side
3m = 21-6
3m=15
m= 15/3
m=5
so, by substituting 5 with m at the original equation we will get:
(x^5(3)) (x^6) = x^21
(x^15)(x^6)=x^21
that applies the same rule to the variable k
k^3(5)=k^15
