Bab 2: Bilangan Berpangkat dan Bentuk Akar

Jawaban Benar: D. $6(2+\sqrt{3})$ Penyelesaian: $\frac{6}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{6(2+\sqrt{3})}{2^2-(\sqrt{3}{)}^2}=\frac{6(2+\sqrt{3})}{4-3}=6(2+\sqrt{3})$

Jawaban Benar: D. $\frac{a^3}{b^5}$ Penyelesaian: $a^{1-(-2)}\cdot b^{-4-1}=a^3\cdot b^{-5}=\frac{a^3}{b^5}$

Jawaban Benar: D. $\frac{a^3}{b^5}$ Penyelesaian: $a^{1-(-2)}\cdot b^{-4-1}=a^3\cdot b^{-5}=\frac{a^3}{b^5}$

Jawaban Benar: B. 3 Penyelesaian: $(2^2{)}^{2x}=(2^3{)}^4$ $2^{4x}=2^{12}$ $4x=12\Rightarrow x=3$

Jawaban Benar: D. $9\sqrt{2}$ Penyelesaian: $3\sqrt{2}+5\sqrt{4\times 2}-\sqrt{16\times 2}$ $=3\sqrt{2}+10\sqrt{2}-4\sqrt{2}$ $=(3+10-4)\sqrt{2}=9\sqrt{2}$

Jawaban Benar: B. $-16k^3{m}^2{n}^7$ Penyelesaian: $(-8\times 2)\cdot k^3\cdot m^2\cdot n^{3+4}=-16k^3{m}^2{n}^7$

Jawaban Benar: D. $\frac{1}{25}$ Penyelesaian: $5^{-2}=\frac{1}{5^2}=\frac{1}{25}$

Jawaban Benar: B. 9 Penyelesaian: $(\frac{1}{3}{)}^{2+(-4)}=(\frac{1}{3}{)}^{-2}=3^2=9$

Jawaban Benar: D. $2^6{t}^2$ Penyelesaian: $2^{3\times 2}\times t^{3+(-1)}=2^6\times t^2=2^6{t}^2$

Jawaban Benar: D. $5\sqrt{3}$ Penyelesaian: $\sqrt{9\times 3}-\sqrt{4\times 3}+\sqrt{16\times 3}$ $=3\sqrt{3}-2\sqrt{3}+4\sqrt{3}$ $=(3-2+4)\sqrt{3}=5\sqrt{3}$

Jawaban Benar: C. $24\sqrt{6}-30\sqrt{3}$ Penyelesaian: $(3\sqrt{2}\times 8\sqrt{3})-(3\sqrt{2}\times 5\sqrt{6})$ $=24\sqrt{6}-15\sqrt{12}$ $=24\sqrt{6}-15(2\sqrt{3})$ $=24\sqrt{6}-30\sqrt{3}$

Jawaban Benar: C. $\frac{1}{64}$ Penyelesaian: $4^{-3}=\frac{1}{4^3}=\frac{1}{4\times 4\times 4}=\frac{1}{64}$

Jawaban Benar: B. 4 Penyelesaian: $(\frac{1}{2}{)}^{3+(-5)}=(\frac{1}{2}{)}^{-2}=2^2=4$

Jawaban Benar: A. $3^6{m}^2$ Penyelesaian: $3^{2\times 3}\times m^{4+(-2)}=3^6\times m^2=3^6{m}^2$

Jawaban Benar: B. $3\sqrt{5}$ Penyelesaian: $\sqrt{4\times 5}-\sqrt{9\times 5}+\sqrt{16\times 5}$ $=2\sqrt{5}-3\sqrt{5}+4\sqrt{5}$ $=(2-3+4)\sqrt{5}=3\sqrt{5}$

Jawaban Benar: A. $8\sqrt{6}-18$ Penyelesaian: $(2\sqrt{3}\times 4\sqrt{2})-(2\sqrt{3}\times 3\sqrt{3})$ $=8\sqrt{6}-6(3)=8\sqrt{6}-18$

Jawaban Benar: A. $\frac{5}{2}(3+\sqrt{5})$ Penyelesaian: $\frac{10}{3-\sqrt{5}}\times \frac{3+\sqrt{5}}{3+\sqrt{5}}=\frac{10(3+\sqrt{5})}{9-5}=\frac{10(3+\sqrt{5})}{4}=\frac{5}{2}(3+\sqrt{5})$

Jawaban Benar: A. $\frac{x^3}{y^4}$ Penyelesaian: $x^{2-(-1)}\cdot y^{-3-1}=x^3\cdot y^{-4}=\frac{x^3}{y^4}$

Jawaban Benar: A. 1 Penyelesaian: $(3^2{)}^{3x}=(3^3{)}^2$ $3^{6x}=3^6\Rightarrow 6x=6\Rightarrow x=1$

Jawaban Benar: A. 10 Penyelesaian: $16+(-8)+4+(-2)=8+2=10$

Jawaban Benar: A. 6 Penyelesaian: $\frac{1}{9}(81-27)=\frac{1}{9}(54)=6$

Jawaban Benar: C. $\sqrt[3]{x^2}\sqrt{y}$ Penyelesaian: $x^{\frac{2}{3}}=\sqrt[3]{x^2}$ dan $y^{\frac{1}{2}}=\sqrt{y}$

Jawaban Benar: A. $15\sqrt{3}$ Penyelesaian: $6\sqrt{12}+\sqrt{9\times 3}$ $=6(2\sqrt{3})+3\sqrt{3}=12\sqrt{3}+3\sqrt{3}=15\sqrt{3}$

Jawaban Benar: A. $5+2\sqrt{6}$ Penyelesaian: $(\sqrt{3}{)}^2+2(\sqrt{3})(\sqrt{2})+(\sqrt{2}{)}^2=3+2\sqrt{6}+2=5+2\sqrt{6}$

Jawaban Benar: A. 17 Penyelesaian: $(5^3{)}^{\frac{2}{3}}-(8^2{)}^{\frac{1}{2}}=5^2-8=25-8=17$