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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4Topics
    |
    2 Quizzes
  2. Properties of Whole Numbers II | Week 2
    4Topics
    |
    2 Quizzes
  3. Properties of Whole Numbers III | Week 3
    4Topics
    |
    1 Quiz
  4. Indices | Week 4
    2Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1Topic
    |
    1 Quiz
Lesson 5, Topic 4
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Law 4: Power of the Base

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1. \( \scriptsize \left( \scriptsize ab\right)^n = a^n \: \times \: b^n \)

2. \( \left(\frac{a}{b} \right)^n = \frac{a^n}{b^n} \)

3. \( \scriptsize \left( \scriptsize a^n\right)^m = a^{n \: \times \: m} \)

e.g

a. \( \scriptsize \left( \scriptsize 2y\right)^3 \\ \scriptsize = 2^3 \: \times \: y^3 \\ \scriptsize = 8y^3 \)

b. \( \left(\frac{2}{y} \right)^3 \\ = \frac{2^3}{y^3}\\ = \frac{8}{y^3} \)

Examples

a.\( \scriptsize \left( \scriptsize 4^2\right)^5 \)

b.\( \scriptsize \left( \scriptsize 10^3\right)^3 \)

c.\( \scriptsize \left( \scriptsize x^4\right)^3 \)

d. \( \left(\frac{2}{3} \right)^2 \)

e. \( \scriptsize \left( \scriptsize 3b\right)^2 \)

f. \( \scriptsize \left(2x^2 \right)^3 \)

Solution

a.\( \scriptsize \left( \scriptsize 4^2\right)^5\\ \scriptsize =4^{2\:\times \: 5} \\ \scriptsize = 4^{10} \)

b.\( \scriptsize \left( \scriptsize 10^3\right)^3 \\ \scriptsize = 10^{3\: \times \: 3} \\ \scriptsize = 10^9 \)

c.\( \scriptsize \left( \scriptsize x^4\right)^3 \\ \scriptsize = x^{4\: \times \: 3} \\ \scriptsize = x^{12} \)

d. \( \left(\frac{2}{3} \right)^2 \\ = \frac{2^2}{3^2} \\= \frac{2\:\times\:2}{3\:\times\:3}\\ = \frac{4}{9} \)

e. \( \scriptsize \left( \scriptsize 3b\right)^2 \\ \scriptsize = 3^2 \: \times \: b^2 \\ \scriptsize = 9 \: \times \: b^2 \\ \scriptsize = 9b^2 \)

f. \( \scriptsize \left(2x^2 \right)^3 \\ \scriptsize= 2^3 \: \times \: x^{2 \: \times \: 3} \\ \scriptsize = 8 \: \times \: x^6 \\ \scriptsize = 8x^6 \)

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