1.2.1 Indeks, Praktis Berformat PT3

1.2.1 Indeks, Praktis Berformat PT3

Soalan 1:

(a) Permudahkan: a⁴÷ a⁷

(b) Nilaikan:

{(2^{4})}^{\frac{1}{2}} \times 3^{\frac{1}{2}} \times 12^{\frac{1}{2}}

Penyelesaian:

(a) a⁴÷ a⁷= a^4-7= a^-3

(b)

\begin{array}{l} {(2^{4})}^{\frac{1}{2}} \times 3^{\frac{1}{2}} \times 12^{\frac{1}{2}} = 2^{2} \times 3^{\frac{1}{2}} \times {(4 \times 3)}^{\frac{1}{2}} \\ = 2^{2} \times 3^{\frac{1}{2}} \times {(2^{2} \times 3)}^{\frac{1}{2}} \\ = 2^{2} \times 3^{\frac{1}{2}} \times 2 \times 3^{\frac{1}{2}} \\ = 2^{3} \times 3 \\ = 24 \end{array}

Soalan 2:

(a) Permudahkan: p³÷ p^-5

(b) Nilaikan:

10^{\frac{1}{2}} \times 5^{- \frac{1}{2}} \times {(2^{\frac{1}{2}})}^{5}

Penyelesaian:

(a) p³÷ p^-5= p^3-(-5)= p³⁺⁵= p⁸

(b)

\begin{array}{l} 10^{\frac{1}{2}} \times 5^{- \frac{1}{2}} \times {(2^{\frac{1}{2}})}^{5} \\ = {(2 \times 5)}^{\frac{1}{2}} \times 5^{- \frac{1}{2}} \times 2^{\frac{5}{2}} \\ = 2^{\frac{1}{2}} \times 5^{\frac{1}{2}} \times 5^{- \frac{1}{2}} \times 2^{\frac{5}{2}} \\ = 2^{\frac{1}{2} + \frac{5}{2}} \times 5^{\frac{1}{2} + (- \frac{1}{2})} \\ = 2^{3} + 5^{\frac{1}{2} - \frac{1}{2}} \\ = 2^{3} + 5^{0} \\ = 8 + 1 \\ = 9 \end{array}

Soalan 3:

(a) Cari nilai bagi

10^{\frac{4}{3}} \div 10^{\frac{1}{3}} .

(b) Permudahkan (xy³)⁵ × x⁴.

Penyelesaian:

(a)

\begin{array}{l} 10^{\frac{4}{3}} \div 10^{\frac{1}{3}} \\ = 10^{\frac{4}{3} - \frac{1}{3}} \\ = 10^{\frac{3}{3}} \\ = 10 \end{array}

\begin{array}{l} (b) {(x y^{3})}^{5} \times x^{4} = x^{5} y^{15} \times x^{4} \\ = x^{5 + 4} y^{15} \\ = x^{9} y^{15} \end{array}

Soalan 4:

(a)

{(81 a^{8})}^{- \frac{1}{4}} =

(b) Cari nilai bagi 2³× 2²

Penyelesaian:

(a)

\begin{array}{l} {(81 a^{8})}^{- \frac{1}{4}} = \frac{1}{{(81 a^{8})}^{\frac{1}{4}}} \\ = \frac{1}{{(3^{4})}^{\frac{1}{4}} {(a^{8})}^{\frac{1}{4}}} \\ = \frac{1}{3 a^{2}} \end{array}

(b)

2³× 2²= 2³⁺²= 2⁵= 32