Answer :

#1

[tex]\\ \rm\rightarrowtail (\dfrac{1}{2})^2=1/4[/tex]

#2

[tex]\\ \rm\rightarrowtail (2/3)^2=4/9[/tex]

#3

[tex]\\ \rm\rightarrowtail -(3/4)^{-2}[/tex]

[tex]\\ \rm\rightarrowtail -(4/3)^2=-16/9[/tex]

semsee45

Answer:

Exponent rules used

[tex]\sf \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}[/tex]

[tex]a^{-b}=\dfrac{1}{a^b}[/tex]

Part (a)

[tex]\sf \left(\dfrac12\right)^2=\dfrac{1^2}{2^2}=\dfrac14[/tex]

Part (b)

[tex]\sf \left(\dfrac23\right)^2=\dfrac{2^2}{3^2}=\dfrac49[/tex]

Part (c)

[tex]\sf -\left(\dfrac34\right)^{-2}=-\left(\dfrac{3^{-2}}{4^{-2}}\right)=-\dfrac{\frac{1}{3^2}}{\frac{1}{{4^2}}}=-\dfrac{\frac19}{\frac{1}{16}}=-\left(\dfrac19 \times \dfrac{16}{1}\right)=-\dfrac{16}{9}[/tex]

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