Y’all high number in the monomial 215x18y3z21 needs to be changed to make it perfect cube

215 should be changed to 216 in order to make perfect cube.

Step-by-step explanation:

 All should be a perfect cube, given

215x^18(y^3)(z^21)

215 cannot be write as cube of a number. Since it is not a perfect cube.

In order to make the perfect cube, we need to change 215 as 216.

6^3 = 6*6*6 = 216

All  variables could make perfect cube.

x^18=(x^6)^3

y^3=y^3

z^21=(z^7)^3

The other terms are perfect cubes except for the first one. So 215 should be changed to 216 in order to make perfect cube.

Hope this will help to understand the concept.

Thank you.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12