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Find the condition for which the formula...

Find the condition for which the formula `(a+b)^m a^m+m a^(m-1)b+(m(m-1))/(1xx2)a^(m-2)b^2+` holds.

A

`a^(2) gt b`

B

`b^(2)lt `

C

`|b| lt |a|`

D

None

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • For any non-zero integers a and b and whole numbers m and n, (a) a^(m)xx a^(n)= a^(m+n) (b) a^(m)+a^(n)= a^(m-n), m gt n= (1)/(a^(n-m)), n gt m (c ) (a^m)^(n)= a^(mn) (d) a^(m)xx b^(m)= (ab)^(m) (e ) a^(m)div b^(m)=(a/b)^(m) (f) a^(0)= 1 (-1)^("even number")=1 (-1)^("odd number")= 1 Simplify and express the following in exponential form. (((6)/(5))^(2)xx x^(8)xx y^(7))+(2^(10)xx (x/3)^(4)xx (y/3)^(3))

    A
    `(3^9)/(5^(2)xx 2^(8))(xy)^(4)`
    B
    `(5^(2)xx 2^(5))/(3^9)(xy)^(4)`
    C
    `((3)/(10))^(4)(xy)^4`
    D
    `(3^9)/(5^(2)xx 2^(8))x^(12)y^(8)`

  • For any non-zero integers a and b and whole numbers m and n, (a) a^(m)xx a^(n)= a^(m+n) (b) a^(m)+a^(n)= a^(m-n), m gt n= (1)/(a^(n-m)), n gt m (c ) (a^m)^(n)= a^(mn) (d) a^(m)xx b^(m)= (ab)^(m) (e ) a^(m)div b^(m)=(a/b)^(m) (f) a^(0)= 1 (-1)^("even number")=1 (-1)^("odd number")= 1 Find the value of (2^(3)+3^(3)+4^(3))xx (1)/((24)^6) .

    A
    `(1)/((24)^3)`
    B
    `((11)/(3^6))`
    C
    `(11)/(3^(4)xx 8^(6))`
    D
    `(33)/((24)^6)`

  • Find the value of the expression (4^(n)+20^(m-1)xx12^(m-n)xx15^(m+n-2))/(16^(m)xx5^(2m+n)xx9^(m-1)) .

    A
    `1/200`
    B
    `1/500`
    C
    `1/700`
    D
    `1/900`

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    For any non-zero integers a and b and whole numbers m and n, (a) a^(m)xx a^(n)= a^(m+n) (b) a^(m)+a^(n)= a^(m-n), m gt n= (1)/(a^(n-m)), n gt m (c ) (a^m)^(n)= a^(mn) (d) a^(m)xx b^(m)= (ab)^(m) (e ) a^(m)div b^(m)=(a/b)^(m) (f) a^(0)= 1 (-1)^("even number")=1 (-1)^("odd number")= 1 Simplify : (25xx 216xx 729)/(6^(6)xx 5^(5)xx 9^(4))

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