Question

Think this can be pretty quick

would also like if someone could help me with the question i asked right before this one (optional)

Answer 1

#1

`\\ \rm\rightarrowtail ((1)/(2))^2=1/4`

#2

`\\ \rm\rightarrowtail (2/3)^2=4/9`

#3

`\\ \rm\rightarrowtail -(3/4)^(-2)`

`\\ \rm\rightarrowtail -(4/3)^2=-16/9`

Answer 2

Exponent rules used

`\sf \left((a)/(b)\right)^c=(a^c)/(b^c)`

`a^(-b)=(1)/(a^b)`

Part (a)

`\sf \left(\frac12\right)^2=(1^2)/(2^2)=\frac14`

Part (b)

`\sf \left(\frac23\right)^2=(2^2)/(3^2)=\frac49`

Part (c)

`\sf -\left(\frac34\right)^(-2)=-\left((3^(-2))/(4^(-2))\right)=-\frac{(1)/(3^2)}{\frac{1}{{4^2}}}=-(\frac19)/((1)/(16))=-\left(\frac19 * (16)/(1)\right)=-(16)/(9)`