(xm. x2)3(k3)5 = x21k15
find the value of m

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

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

0.6

39mph

step-by-step explanation: