Pertanyaan

Pangkat

1. 8p²q × 2pq³
2. 64^1⁄₂ + 81^1⁄₃
3. 25 + 320 - 45

Merasionalkan Akar

4. ⁴⁄₅
5. ³⁵⁄₂₃
6. ⁵⁄_{3 - 2}
7. ^{5 - 7}⁄_{5 - 2}

Operasi Pangkat

8. (8p²3)³ ÷ 2pq
9. ^{(a1⁄₃b1⁄₃)6}⁄_{(a^2⁄3b^4⁄3)⁹}

Persamaan Pangkat

10. 2^{x + 8} = 64
11. 16^{2x + 3} = 32

Jawaban

1. 16p³q⁴
2. 64^1⁄₂ + 81^1⁄₃
   = 64 + ³81
   = 8 + ³81
3. 25 + 320 - 45
   = 65 + 320
   = 65 + 34 × 5
   = 65 + 32² × 5
   = 65 + 3 × 25
   = 65 + 65
   = 125
   
4. ⁴⁄₅
   = ⁴⁄₅ × ⁵⁄₅ = ⁴⁵⁄₅
5. ³⁵⁄₂₃
   = ³⁵⁄₂₃ × ³⁄₃
   = ³¹⁵⁄_{2 × 3}
   = ¹⁵⁄₂
6. ⁵⁄_{3 - 2}
   = ⁵⁄_{3 - 2} × ^{3 + 2}⁄_{3 + 2}
   = ^{5(3 + 2)}⁄_{(3)² - (2)²}
   = ^{5(3 + 2)}⁄_{3 - 2} = ^{5(3 + 2)}⁄₁
   = 5(3 + 2)
7. ^{5 - 7}⁄_{5 - 2}
   = ^{5 - 7}⁄_{5 - 2} × ^{5 + 2}⁄_{5 + 2}
   = ^{(5 - 7) × (5 + 2)}⁄_{(5)² - (2)²}
   = ^{5 + 10 - 35 - 14}⁄_{5 - 2} = ^{5 + 10 - 35 - 14}⁄₃
8. (8p²3)³ ÷ 2pq
   = (24p²)³ ÷ 2pq
   = 24³ p⁶ ÷ 2pq
   = 6912p⁵ ÷ q
9. = ^{(a1⁄₃b1⁄₃)6}⁄_{(a^2⁄3b^4⁄3)⁹}
   = ^{(a1⁄₃)6 (b1⁄₃)6} ⁄ _{(a^2⁄3)⁹ (b^4⁄3)⁹}
   = ^{a2 b2} ⁄ _{a⁶ b¹²}
   = a^-4 b^-10
10. 2^{x + 8} = 64
    = 2^{x + 8} = 2⁶
    = x + 8 = 6
    = x = 6 - 8
    = x = -2
11. 16^{2x + 3} = 32
    = (2⁴)^{2x + 3} = 2⁶
    = 2^{8x + 12} = 2⁶
    = 8x + 12 = 6
    = 8x = 6 - 12
    = 8x = 6
    = x = ^-6⁄₈
    = x = -³⁄₄