x?? i need answers asap! ten points for first detailed answer!?

Question

a) verify that x^2 x x^3 = x^5

b) suggest a rule for x^a x x^b
c) verify that x^7 /x^3 = x^4
d) suggest a rule for x^a / x^b
e) By letting a=b, use d) to show that x^0 = 1.

Answer 1

x^n implies that x is multiplied by itself 'n' times.



a) x^2 x x^3 = (x*x)*(x*x*x) = x*x*x*x*x = x^(2+3) = x^5



b) x^a x x^b = (x is multiplied by itself 'a' times) * (x is multiplied by itself 'b' times) = x is multiplied by itself '(a+b)' times = x^(a+b)



c) x^7 / x^3 = (x is multiplied by itself '7' times) / (x is multiplied by itself '3' times) = (x*x*x*x*x*x*x) / (x*x*x) = (x*x*x*x) = x^(7-3) = x^4



d) x^a / x^b = (x is multiplied by itself 'a' times) / (x is multiplied by itself 'b' times) = x is multiplied by itself '(a-b)' times = x^(a-b)



e) when a=b is substituted in (d) we get

x^a / x^a = x^(a-a)

=> 1 = x^0

Answer 2

a) because powers 2+3 =5

b) x^a+b

c) because 7-3=4



d) x^a-b

e) any number to the power 0 =1

Answer 3

a) yes correct!! x^2*x^3=x^2+3=x^5

b) x^a*x^b= x^a+b

c)correct x^7/x^3=x^7-3=x^4

d)x^a/x^b = x^a-b

e)if a=b=4

then : x^4/x^4=x^4-4=x^0=1



^^

Answer 4

a)

x^2 = x*x

x^3 = x*x*x

So x^2*x^3 = (x*x)*(x*x*x) =x*x*x*x*x = x^5



b) x^a*x^b = (x*x (a times))*(x*x (b times))=x*x (a+b times) = x^(a+b)



c) x^7/x^3 = x*x*x*x*x*x*x/x*x*x = x*x*x*x = x^4



d)x^a/x^b=(x*x a times)/(x*x b times) = (x*x a-b times) = x^(a-b)



e) let a=b=3

x^3/x^3 = x*x*x/x*x*x = 1

but x^3/x^3 = x^(3-3) = x^0 therefore x^0 = 1

Answer 5

a) (x^2)(x^3) = (x)(x)(x)(x)(x) = x^5

b) x^(a+b)

c) x^7 /x^3 = (x)(x)(x)(x)(x)(x)(x) / (x)(x)(x) = x^4

d) x^(a-b)

e) x^0 = x^(a-b) = x^(a-a) = (x^a) / (x^a) = 1

Answer 6

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