Math Problem Statement

Multiple-choice math questions from an image, including powers, square roots, and quadratic equations.

Solution

I see the image contains a series of multiple-choice math questions. I will provide solutions for each question.

Solutions:

  1. Hasil dari 23×242^3 \times 2^4 adalah... 23×24=23+4=272^3 \times 2^4 = 2^{3+4} = 2^7 Jawaban: a. 2^7

  2. Bentuk sederhana dari (a2)3(a^2)^3 adalah... (a2)3=a2×3=a6(a^2)^3 = a^{2 \times 3} = a^6 Jawaban: b. a^6

  3. Nilai dari 125\sqrt{125} adalah... 125=25×5=25×5=55\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5} Jawaban: d. 5\sqrt{5}

  4. Bentuk sederhana dari 32+523\sqrt{2} + 5\sqrt{2} adalah... 32+52=(3+5)2=823\sqrt{2} + 5\sqrt{2} = (3 + 5)\sqrt{2} = 8\sqrt{2} Jawaban: a. 8\sqrt{2}

  5. Bentuk baku dari 5.000.000 adalah... 5.000.000=5×1065.000.000 = 5 \times 10^6 Jawaban: d. 5 \times 10^6

  6. Bilangan 6,78×1046,78 \times 10^4 jika ditulis dalam bentuk biasa adalah... 6,78×104=678006,78 \times 10^4 = 67800 Jawaban: a. 67.800

  7. Bentuk baku dari 0,000000078 adalah... 0,000000078=7,8×1080,000000078 = 7,8 \times 10^{-8} Jawaban: c. 7,8 \times 10^{-8}

  8. Bilangan 2,5×1052,5 \times 10^5 jika dikalikan dengan 4×1034 \times 10^3 hasilnya adalah... 2,5×105×4×103=(2,5×4)×105+3=10×108=1×1092,5 \times 10^5 \times 4 \times 10^3 = (2,5 \times 4) \times 10^{5+3} = 10 \times 10^8 = 1 \times 10^9 Jawaban: b. 1 \times 10^9

  9. Jarak antara Bumi dan Matahari sekitar 1,5×10111,5 \times 10^{11} meter. Jika ditulis dalam bentuk biasa, jarak tersebut adalah... 1,5×1011=150.000.000.0001,5 \times 10^{11} = 150.000.000.000 Jawaban: d. 150.000.000.000 meter

  10. Bentuk rasional dari 352\frac{3}{\sqrt{5} - 2} adalah... Mengalikan dengan sekawan: 352×5+25+2=3(5+2)(52)(5+2)=3(5+2)54=3(5+2)\frac{3}{\sqrt{5} - 2} \times \frac{\sqrt{5} + 2}{\sqrt{5} + 2} = \frac{3(\sqrt{5} + 2)}{(\sqrt{5} - 2)(\sqrt{5} + 2)} = \frac{3(\sqrt{5} + 2)}{5 - 4} = 3(\sqrt{5} + 2) Jawaban: b. 35+63\sqrt{5} + 6

Let me know if you want the complete solutions for the remaining questions or have any specific queries.

5 Relative Questions:

  1. How do you rationalize a denominator in a fraction?
  2. Can you explain how to convert a number into standard form?
  3. How do you add and simplify like terms with radicals?
  4. What are the rules for multiplying exponents?
  5. How do you solve quadratic equations?

Tip:

When dealing with exponents, always remember the basic rules like am×an=am+na^m \times a^n = a^{m+n} and (am)n=am×n(a^m)^n = a^{m \times n}.

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Math Problem Analysis

Mathematical Concepts

Exponents
Square Roots
Scientific Notation
Quadratic Equations

Formulas

a^m * a^n = a^(m+n)
sqrt(a*b) = sqrt(a) * sqrt(b)
Quadratic equation: ax^2 + bx + c = 0
Scientific notation: a * 10^n

Theorems

Laws of Exponents
Quadratic Formula

Suitable Grade Level

Grades 7-9