Question

plz help step by step​

Answer 1

(i) $\sf (4^{2}-3^{2})\times (\frac{7}{2})^{-2}$

Step 1: Give appropriate values for numbers in brackets.

⇒ $\sf (16-9)\times (\frac{7}{2} )^{-2}$

Step 2: We have to apply this law ⇒ $\sf a^{-m}=\frac{1}{a^{m}}$

⇒ $\sf (16-9)\times (\frac{2}{7} )^{2}$

Step 3: Solve brackets.

⇒ $\sf 7 \times \frac{4}{49}$

Step 4: Multiply the numbers.

⇒ $\sf 7 \times \frac{4}{49}$

⇒ $\sf \frac{28}{49}$

Step 5: Simplify the fraction.

⇒ $\sf \frac{28\div 7 }{49\div 7 }$

⇒ $\sf \frac{4}{7}$

$\sf \bf \therefore (4^{2}-3^{2})\times (\frac{7}{2})^{-2} = \frac{4}{7}$

(ii) $\sf (5^{-1}\times 6^{-1})\div 10^{-1}$

Step 1: Apply this law in the brackets ⇒ $\sf a^{-m}=\frac{1}{a^{m}}$

⇒ $\sf (\frac{1}{5} \times \frac{1}{6} )\div 10^{-1}$

Step 2: Solve the brackets.

⇒ $\sf \frac{1}{30} \div 10^{-1}$

Step 3: Apply this law ⇒ $\sf a^{-m}=\frac{1}{a^{m}}$

⇒ $\sf \frac{1}{30}\div \frac{1}{10}$

Step 4: Divide the fractions.

⇒ $\sf \frac{1}{30}\times 10$

⇒ $\sf \frac{10}{30}$

Step 5: Simplify the fractions.

⇒ $\sf \frac{10\div 10 }{30\div 10 }$

⇒ $\sf \frac{1}{3}$

$\sf \bf \therefore (5^{-1}\times 6^{-1})\div 10^{-1}$