Soalan 3:
$$ \text { Diberi bahawa } m=2 \text { dan } n=-3 \text {. Hitung nilai bagi } 64^{\frac{m}{3}} \times 512^{\left(-\frac{1}{n}\right)} \div 81^{\frac{n}{2 m}} \text {. } $$
Penyelesaian:
$$ \begin{aligned} &64^{\frac{m}{3}} \times 512^{\left(-\frac{1}{n}\right)} \div 81^{\frac{n}{2 m}}\\ &\text { Diberi } m=2 \text { dan } n=-3 \end{aligned} $$
$$ \begin{aligned} 64^{\frac{2}{3}} \times 512\left(-\frac{1}{-3}\right) \div 81^{\frac{-3}{2(2)}} & =\left(4^3\right)^{\frac{2}{3}} \times 512^{\frac{1}{3}} \div 81^{-\frac{3}{4}} \\ & =4^2 \times 8^{3 \times \frac{1}{3}} \div 3^{4 \times-\frac{3}{4}} \\ & =2^4 \times 8 \div 3^{-3} \\ & =2^4 \times 2^3 \div \frac{1}{3^3} \\ & =2^{4+3} \times 3^3 \\ & =2^7 \times 3^3 \\ & =3456 \end{aligned} $$
$$ \text { Diberi bahawa } m=2 \text { dan } n=-3 \text {. Hitung nilai bagi } 64^{\frac{m}{3}} \times 512^{\left(-\frac{1}{n}\right)} \div 81^{\frac{n}{2 m}} \text {. } $$
Penyelesaian:
$$ \begin{aligned} &64^{\frac{m}{3}} \times 512^{\left(-\frac{1}{n}\right)} \div 81^{\frac{n}{2 m}}\\ &\text { Diberi } m=2 \text { dan } n=-3 \end{aligned} $$
$$ \begin{aligned} 64^{\frac{2}{3}} \times 512\left(-\frac{1}{-3}\right) \div 81^{\frac{-3}{2(2)}} & =\left(4^3\right)^{\frac{2}{3}} \times 512^{\frac{1}{3}} \div 81^{-\frac{3}{4}} \\ & =4^2 \times 8^{3 \times \frac{1}{3}} \div 3^{4 \times-\frac{3}{4}} \\ & =2^4 \times 8 \div 3^{-3} \\ & =2^4 \times 2^3 \div \frac{1}{3^3} \\ & =2^{4+3} \times 3^3 \\ & =2^7 \times 3^3 \\ & =3456 \end{aligned} $$
Soalan 4:
$$ \text { Diberi bahawa } a=\frac{1}{2} \text { dan } b=\frac{2}{3} \text {. Hitung nilai bagi } 144^a \div 64^b \times 256^{\frac{a}{b}} \text {. } $$
Penyelesaian:
$$ \begin{aligned} &144^a \div 64^b \times 256^{\frac{a}{b}}\\ &\text { Diberi } a=\frac{1}{2} \text { dan } b=\frac{2}{3} \end{aligned} $$
$$ \begin{aligned} 144^{\frac{1}{2}} \div 64^{\frac{2}{3}} \times 256^{\frac{\frac{1}{2}}{\frac{2}{3}}} & =12^{2 \times \frac{1}{2}} \div 4^{3 \times \frac{2}{3}} \times 256^{\frac{1}{2} \times \frac{3}{2}} \\ & =12 \div 4^2 \times 256^{\frac{3}{4}} \\ & =\frac{12}{4^2} \times 4^{4 \times \frac{3}{4}} \\ & =\frac{12}{4^2} \times 4^3 \\ & =12 \times 4^{3-2} \\ & =12 \times 4 \\ & =48 \end{aligned} $$
$$ \text { Diberi bahawa } a=\frac{1}{2} \text { dan } b=\frac{2}{3} \text {. Hitung nilai bagi } 144^a \div 64^b \times 256^{\frac{a}{b}} \text {. } $$
Penyelesaian:
$$ \begin{aligned} &144^a \div 64^b \times 256^{\frac{a}{b}}\\ &\text { Diberi } a=\frac{1}{2} \text { dan } b=\frac{2}{3} \end{aligned} $$
$$ \begin{aligned} 144^{\frac{1}{2}} \div 64^{\frac{2}{3}} \times 256^{\frac{\frac{1}{2}}{\frac{2}{3}}} & =12^{2 \times \frac{1}{2}} \div 4^{3 \times \frac{2}{3}} \times 256^{\frac{1}{2} \times \frac{3}{2}} \\ & =12 \div 4^2 \times 256^{\frac{3}{4}} \\ & =\frac{12}{4^2} \times 4^{4 \times \frac{3}{4}} \\ & =\frac{12}{4^2} \times 4^3 \\ & =12 \times 4^{3-2} \\ & =12 \times 4 \\ & =48 \end{aligned} $$