Question

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

Answer 1

★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