Question

Evaluate (5-¹×4-¹)×(3/2)-²​

Answer 1

Answer:

$\sf{}\dfrac{1}{90}$

Explanation:

$\Rightarrow\sf{}(5^-1\times4^{-1})\times \bigg(\dfrac{3}{2}\bigg)^{-2}$

$\sf{}\Rightarrow\bigg(\dfrac{1}{5}\bigg) ^{1}\times\bigg(\dfrac{1}{4}\bigg) ^{1}\times\bigg(\dfrac{2}{3}\bigg) ^{2}$

$\sf{}\Rightarrow \dfrac{1}{5}\times \dfrac{1}{4}\times \dfrac{2}{9}$

$\Rightarrow \dfrac{2}{180}$

$\sf{}\Rightarrow \dfrac{1}{90}$

$\bigstar \sf{}Laws\ of\ exponent}\bigstar [For\ a\neq0,b\neq0]$

$1)a^x\times a^y=a^{x+y}$

$2)a^x\div a^y=a^{x-y}$

$3)(a^x)^y=a^{xy}$

$4)a^0=1$

$5)a^{-1}=\dfrac{1}{a}$

$6)\bf \sqrt[n]{ \sqrt[m]{ \sqrt[p]{((a^{x} )^{y}) ^{z} } } } = (a ^{xyz} )^{ \frac{1}{mnp} } = a ^{ \frac{xyz}{mnp} }$

Answer 2

Question:-

➣ Evaluate:-

Answer:-

➣

$({5}^{-1} × {4}^{-1})$× $(\frac{3}{2})^{-2}$

Solution:-

➣

➣$({5}^{-1} × {4}^{-1})$ × $(\dfrac{3}{2})^{-2}$

➣$(\dfrac{1}{5}) ^{1}\times(\dfrac{1}{4}) ^{1}\times(\dfrac{2}{3}) ^{2}$

➣$\dfrac{1}{5}\times \dfrac{1}{4}\times \dfrac{2}{9}$

➣$\dfrac{2}{180}$

➣$\cancel{\dfrac{2}{180}}$

➣$\dfrac{1}{90}$

➣$\huge{\purple{\dfrac{1}{90}}}$