Question

Find the value of 36to the power7/2-36 to the power 9/2 divided by 36 to the power 5/2

Answer 1

Answer:

$\bf\displaystyle\frac{36^{\frac{7}{2}}-36^{\frac{9}{2}}}{36^{\frac{5}{2}}}=-1260$

Step-by-step explanation:

$\displaystyle\frac{36^{\frac{7}{2}}-36^{\frac{9}{2}}}{36^{\frac{5}{2}}}$

$=\displaystyle\frac{(6^2)^{\frac{7}{2}}-(6^2)^{\frac{9}{2}}}{(6^2)^{\frac{5}{2}}}$

$=\displaystyle\frac{6^7-6^9}{6^5}$

$=\displaystyle\frac{6^5(6^2-6^4)}{6^5}$

$=6^2-6^4$

$=36-1296$

$=-1260$

$\implies\boxed{\bf\displaystyle\frac{36^{\frac{7}{2}}-36^{\frac{9}{2}}}{36^{\frac{5}{2}}}=-1260}$