If a = 2^m and b = 2^m+1 , the value of 8a^3/b^2 will be???​

Question

If a = 2^m and b = 2^m+1 , the value of 8a^3/b^2 will be???​

in progress 0
Savannah 1 month 2021-08-13T11:38:31+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-13T11:39:49+00:00

    Given:

    • \sf 2^m = a
    • \sf 2^{m+1} = b

    To find:

    • \sf \dfrac{8a^3}{b^2}

    Solution:

    \sf \implies\dfrac{8a^3}{b^2}

    \sf \implies\dfrac{(2a)^3}{b^2}

    \sf \implies\dfrac{(2 \times 2^m)^3}{(2^{m+1})^2}

    \sf \implies\dfrac{( 2^{m+1})^3}{(2^{m+1})^2} \qquad\qquad ..[as \ 2^{1+1} = 2 \times 2 ]

    Here, bases [ 2^{m+1}] are same so the powers will be subtracted on division.

    \sf \implies (2^{m+1})^3 \div (2^{m+1})^2

    \sf \implies (2^{m+1})^{3-2}

    \sf \implies (2^{m+1})^{1}

    \sf \implies 2^{m+1}

    \bf \therefore \qquad\dfrac{8a^3}{b^2} = 2^{m+1}

    Hope it helps

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )