Soal Sifat-Sifat Eksponen 02

Jawaban: A

Soal dapat ditulis:

\(\dfrac{(-2x^2y)^3}{x^5y \cdot (-2x^2y^2)}\)

\(\dfrac{-2^3 \cdot x^6 \cdot y^3}{-2 \cdot x^7 \cdot y^3}\)

\(\dfrac{\cancelto{4}{-8} \cdot x^6 \cdot \cancel{y^3}}{\cancel{-2} \cdot x^7 \cdot \cancel{y^3}}\)

\(\dfrac{4 \cdot x^6}{x^7}\)

\(\dfrac{4 \cdot \cancel{x^6}}{\cancelto{x}{x^7}}\)

\(\color{red}\dfrac{4}{x}\)

Jawaban: D

\(3^x + 3^{-x} = 10\:\:\:\:\:\color{blue}\text{kuadratkan kedua ruas}\)

\((3^x + 3^{-x})^2 = 10^2\)

\(3^{2x}  + 2\cdot 3^x \cdot 3^{-x} + 3^{-2x} = 100\)

\(3^{2x} + 2 + 3^{-2x} = 100\)

\(3^{2x} + 3^{-2x} = 100 \:-\: 2\)

\(3^{2x} + 3^{-2x} = 98\)

Jawaban: A

\(2^x + 2^{-x} = 7\:\:\:\:\:\color{blue}\text{kedua ruas dipangkatkan tiga}\)

\((2^x + 2^{-x})^3 = 7^3\)

Catatan: \(\color{blue}(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\)

\(2^{3x} + 3\cdot 2^{2x} \cdot 2^{-x} + 3 \cdot 2^x \cdot 2^{-2x} + 2^{-3x} = 343\)

\(2^{3x} + 2^{-3x} + 3\cdot 2^{(2x\: – \: x)}+ 3 \cdot 2^{(x \:- \:2x)} = 343\)

\(2^{3x} + 2^{-3x} + 3(2^x+ 2^{-x}) = 343\)

\(2^{3x} + 2^{-3x} + 3(7) = 343\)

\(2^{3x} + 2^{-3x} + 21 = 343\)

\(2^{3x} + 2^{-3x} = 343\:-\: 21\)

\(2^{3x} + 2^{-3x} = 322\)

Jawaban: C

\(8^{1-xyz} = \dfrac{8}{8^{xyz}}\)

\(8^{1-xyz} = \dfrac{8}{2^{3(xyz)}}\)

\(8^{1-xyz} = \dfrac{8}{2^{x(3yz)}}\)

\(8^{1-xyz} = \dfrac{8}{3^{y(3z)}}\)

\(8^{1-xyz} = \dfrac{8}{4^{3z}}\)

\(8^{1-xyz} = \dfrac{8}{5^3}\)

\(8^{1-xyz} = \dfrac{8}{125}\)

Jawaban: A

\(\left(\dfrac{1}{x^{-1} + y^{-1}}\right)\left(\dfrac{xy^{-1} \: – \:x^{-1}{y}}{y^{-1}\: – \:x^{-1}}\right)\)

\(\left(\dfrac{1}{\frac{1}{x} + \frac{1}{y}}\right)\left(\dfrac{\frac{x}{y} \: – \: \frac{y}{x}}{\frac{1}{y}\: -\: \frac{1}{x}}\right)\)

\(\left(\dfrac{1}{\frac{x + y}{xy}}\right)\left(\dfrac{\frac{x^2 \:-\: y^2}{xy}}{\frac{x\:-\:y}{xy}}\right)\)

\(\left(\dfrac{xy}{\cancel{x+y}}\right)\left(\dfrac{\frac{\cancel{(x + y)}\cancel{(x\:-\:y)}}{\cancel{xy}}}{\frac{\cancel{x\:-\:y}}{\cancel{xy}}}\right)\)

\(xy\)