Question

copy me solve kr k batana please​

Answer 1

Question :

• $\left(\dfrac{64^{-1}}{64^{-7}}\right) ^7$

Solution :

$\sf \longmapsto \left(\dfrac{64^{-1}}{64^{-7}}\right) ^7$

❍ We know that,

$\red\bigstar\:\boxed{\sf\dfrac{a^m}{a^n}} = a^{m-n}$

❍ Applying this Identity here,

$\dashrightarrow \left( 64^{(-1) -(-7)} \right)^7 \\\\\dashrightarrow \left( 64^{-1+7} \right)^7 \\\\\dashrightarrow \left( 64^6 \right) ^7$

❍ We also know that,

$\red\bigstar\:\boxed{\sf (a^m)^n = a^{m\times n} }$

❍ Applying this Identity here,

$\longmapsto \left( 64^6 \right) ^7 \\\\\dashrightarrow 64^{6 \times 7} \\\\\dashrightarrow \pink{64^{42}}$

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More to know :

• $\sf a^m\times a^n = a^{m+n}$
• $\sf (a^m)^n = a^{mn}$
• $\sf a^1 = a$
• $\sf a^0 = 1$
• $\sf a^{-m}=\frac{1}{a^m}$
• $\sf a^{m/n}=\sqrt[m]{a^n} = \sqrt[m]{a}\;^n$
• $\sf a^m = a^n \: , then \: m= n$