Question

please guys tell me the answers​

Answer 1

(i) Let's solve using BODMAS

So first we solve simple brackets (in simple brackets, we do subtraction)  and then box brackets (in the box brackets, we do division).

⇒ $\sf [(3^2-2^2)\div \frac{1}{5}]^2$

⇒ $\sf [(9-4)\div \frac{1}{5}]^2$

⇒ $\sf [5\div \frac{1}{5}]^2$

⇒ $\sf [5\times 5]^2$

⇒ $\sf 25^2$

⇒ $\sf 625$

∴ $\sf \bf [(3^2-2^2)\div \frac{1}{5}]^2=625$

(ii) For this question, we need to apply laws of exponents.

First, we will use this law ⇒ $\sf (a^m)^n = a^{m\times n}$

$\sf ((5^2)^3\times 5^4)\div 5^6$

$\sf (5^{2\times 3} \times 5^4)\div 5^6$

$\sf (5^{6} \times 5^4)\div 5^6$

Now, we will use this law ⇒ $\sf a^m\times a^n = a^{m+n}$

$\sf (5^{6} \times 5^4)\div 5^6$

$\sf (5^{6+4})\div 5^6$

$\sf 5^{10}\div 5^6$

At last, we will use this law ⇒ $\sf a^m \div a^n = \frac{a^m}{a^n} = a^{m-n}$

$\sf 5^{10}\div 5^6$

$\sf 5^{10-6}$

$\sf 5^4$

$\sf 625$

∴ $\sf \bf ((5^2)^3\times 5^4)\div 5^6 = 625$