Question

solve by using law of exponenrs​

Answer 1

Answer:

(1/2)⁻² ÷ (1/2)³

= (1/2)⁻²⁻³

= (1/2)⁻⁵

= 2⁵

= 32

[(1/3)²]³  x (1/3)⁻⁶

= (1/3)⁶ x (1/3)⁻⁶

= (1/3)⁶⁻⁶

= (1/3)°

= 1

Answer 2

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge{\boxed{\bullet{\color{coral}{\mathcal{ANSWER}}}\bullet}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$

✯ Laws of Exponents :-

• ${a}^{m} × {a}^{n} = {a}^{m+n}$

• $\frac{{a}^{m}}{{a}^{n}} = {a}^{m-n}$

• $({{a}^{m}})^{n} = {a}^{mn}$

• ${a}^{0} = 1$

• ${a}^{-m} = \frac{1}{{a}^{m}}$

Now, Let's solve the questions using these laws of Exponents :-

Q1. $({\frac{1}{2}})^{-2} ÷ ({\frac{1}{2}})^{3}$

➙ Now, using $\frac{{a}^{m}}{{a}^{n}} = {a}^{m-n}$

➙ $({\frac{1}{2}})^{-2-3}$

➙ $({\frac{1}{2}})^{-5}$

➙ Now using, ${a}^{-m} = \frac{1}{{a}^{m}}$

➙ ${(2)}^{5}$

➙ 32

Q2. $[{( { \frac{1}{3} })^{2}}]^{3} × {\frac{1}{3}}^{-6}$

➙ Now using, $({{a}^{m}})^{n} = {a}^{mn}$

➙ $({\frac{1}{3}})^{6} × ({\frac{1}{3}})^{-6}$

➙ Now using, ${a}^{m} × {a}^{n} = {a}^{m+n}$

➙ $({\frac{1}{3}})^{6+(-6)}$

➙ $({\frac{1}{3}})^{0}$

➙ Now using, ${a}^{0} = 1$

➙ 1