Question

Q-2 Solve the following problems.​

Answer 1

Answer:

Answer is attached here

Answer 2

1. To simplify $(\dfrac{5}{2})^{5}\div (\dfrac{2}{5})^{3}$

Step-by-step explanation:

Now, $(\dfrac{5}{2})^{5}\div (\dfrac{2}{5})^{3}$

$=(\dfrac{5}{2})^{5}\times (\dfrac{5}{2})^{3}$

• since $\div$ changes into $\times$ and the later fraction becomes reciprocal

$=(\dfrac{5}{2})^{5+3}$

• since $a^{b}\times a^{c}=a^{b+c}$

$=(\dfrac{5}{2})^{8}$

$=\dfrac{390625}{256}$

2. To simplify $\dfrac{a^{4}\times b^{5}\times c^{7}}{c^{8}\times a^{4}\times b^{3}}$

Step-by-step explanation:

Now, $\dfrac{a^{4}\times b^{5}\times c^{7}}{c^{8}\times a^{4}\times b^{3}}$

$=\dfrac{a^{4}\times b^{5}\times a^{-4}\times b^{3}}{c^{8}\times c^{-7}}$

$=\dfrac{a^{4-4}\times b^{5-3}}{c^{8-7}}$

$=\dfrac{a^{0}\times b^{2}}{c^{1}}$

$=\dfrac{b^{2}}{c}$

• since $a^{0}=1$

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