#1 what is the value of the expression 7–3? answers: a. –21b. - 1/343 c.1/343 d. 343 #2what is the value of the expression 1/5^-5? answers: a. 1/3125 b.1/25 c.25 d. 3125 #3what is the value of the expression 2/4^-3? answers: a. 1/32 b. 1/6 c.128 d.256 #4 what value of k solves the equation? k^-2=1/64 answers: a.1/8 b. 8 c. 32 d. 128 #5 what value of n solves the equation? 4^n= 1/64 answers: a. –3 b. 3 c. 16 d. 256

First question

The given expression is

Which can also be written as

Therefore the correct option is C.

2.

The given expression is

Which can also be written as

So the correct option is D

3.

The given expression is

Which can also be written as

And the correct option is C

4.

The given equation is

So the correct option is B

5.

The given equation is

And the correct option is A .

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