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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 5
In Progress

Law 5: Zero Index

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This law states that any number raised to the power of zero (0) equals 1.

\( \scriptsize a^{0} = 1 \)

\( \scriptsize m^{0} = 1 \)

\( \scriptsize 10^{0} = 1 \)

Example

Simplify the following;

a. \( \scriptsize 4^{0} \)

b. \( \scriptsize\left( 5^6\right)^{0} \)

c. \( \scriptsize 5^2 \: \times \: 5^{-2}\)

d. \( \scriptsize 2^5 \: \div \: 2^{5}\)

e. \( \scriptsize 8a^0 \: \div \: 8^{0}\)

Solution

a. \( \scriptsize 4^{0} = 1\)

b. \( \scriptsize\left( 5^6\right)^{0} = 1 \)

c. \( \scriptsize 5^2 \: \times \: 5^{-2} \\ \scriptsize =5^{2-2} \\ \scriptsize = 5^0 \\ \scriptsize = 1\)

d. \( \scriptsize 2^5 \: \div \: 2^{5} \\ \scriptsize = 2^{5-5} \\ \scriptsize = 2^0 \\ \scriptsize = 1\)

e. \( \scriptsize 8a^0 \: \div \: 8^{0} \\ \scriptsize 8 \: \times \: a^0 \: \div \: 8^o \\ \scriptsize = 8 \: \times \: 1 \: \div \: 1\\ \scriptsize = 8 \: \div \: 1 \\ \scriptsize = 8\)

Evaluation

1. Simplify the following by 

(i) expansion of terms 

(ii) law of indices

a. \( \scriptsize 3^4\: \times \: 3^2 \)

b. \( \scriptsize a^3\: \times \: a^4 \)

c. \( \scriptsize 5^3\: \times \: 5 \: \times \: 5^6 \)

d. \( \frac{(3)^4}{4} \: \times \: \frac{(3)^3}{4}\)

e. \( \scriptsize Z \: \times \: Z \)

f. \( \scriptsize x^5\: \times \: x \: \times \: x \)

g. \( \scriptsize c \: \times \: c\: \times \: c^2 \: \times \: c^3\: \times \: c^4 \)

h. \( \scriptsize 8^2 \: \times \: 8^2 \: \times \: 8^3 \)

View Answers

2. Simplify the following

a. \( \scriptsize 2q^7 \: \times \: 3q^8 \: \times \: 4q\)

b. \(\normalsize \frac{2}{5} \scriptsize m^2 \: \times \: \normalsize \frac{5}{7} \scriptsize m^7 \)

c. \( \scriptsize 8y^2 \: \times \: 7y^3 \)

d. \( \scriptsize 7n^3 \: \times \: n^{\frac{1}{2}}\)

View Answers

3. Simplify the following by 

i. expansion

ii. laws of indices

a. \(\scriptsize 15^5 \: \div \: 15^4\)

b. \(\scriptsize 4^7 \: \div \: 4^3\)

c. \(\scriptsize 3^{12} \: \div \: 3^7\)

d. \(\scriptsize 12^{5} \: \div \: 15\)

e. \(\scriptsize 20y^{14} \: \div \: 5y^5\)

f. \(\scriptsize 35d^{17} \: \div \: 7d^{10}\)

g. \(\scriptsize 3x^{3} \: \div \: 6x\)

h. \(\scriptsize 7d^{8} \: \div \: 38d^5\)

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4. (A) Simplify the following by 

i. expansion

ii. the law of negative index

a. \( \scriptsize 10^{-5} \)

b. \( \scriptsize 7^{-3} \)

c. \( \scriptsize 9^2 \: \div \: 9^4 \)

d. \( \scriptsize x^5 \: \times \: x^{-7} \)

e. \( \scriptsize (1.5)^{-2} \)

f. \( \scriptsize 10^{12} \: \div \: 10^{15} \)

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4(B) Simplify the following

a. \( \scriptsize 5a{-3} \: \times \: 4b \)

b. \(\scriptsize (7x)^{-2} \)

c. \( \scriptsize 5a^{-1} \: \times \: a^{-3} \)

d. \( \scriptsize 2^{-3} \:\times \: 2^{-2} \: \times \: 2^4 \)

e. \( \left(\frac{1}{8} \right)^{-2} \: \times \: \left( \frac{1}{2}\right)^3 \)

f. \( \scriptsize 2g^6 \: \div \: 4g^7 \)

View Answers

5. Evaluate the following leaving your answer in index form when necessary.

a. \( \scriptsize (5^3)^5 \)

b. \( \scriptsize ((2x)^4)^3 \)

c. \( \scriptsize (0.5^2)^3 \)

d. \( \left(\frac{1}{2y} \right)^{-2} \)

e. \( \left(\frac{5}{x} \right)^3 \)

f. \( \scriptsize (5y)^3 \: \times \: y^{-10} \)

6. Simplify the following

a. \( \scriptsize 13^0 \)

b. \( \scriptsize 1.3^0 \)

c. \( \scriptsize 7^{-2} \: \times \: 7^2 \: \times \: 7^0\)

d. \( \scriptsize (2x)^0 \: \div \: x^3 \)

e. \( \scriptsize 5x^2 \: \times \: (2x)^{-2} \)

f. \( \frac{(5^{10})^0}{5^4} \)

Answers

a. \( \scriptsize 3^6 \)

b. \( \scriptsize a^7 \)

c. \( \scriptsize 5^{10} \)

d. \( \frac{3^7}{4^2} \)

e. \( \scriptsize Z^2 \)

f. \( \scriptsize x^7 \)

g. \( \scriptsize c^{11} \)

h. \( \scriptsize 8^7\)

Answers

a. \( \scriptsize 24^{16} \)

b. \( \frac{2}{7} \scriptsize m^9\)

c. \( \scriptsize 56y^{5} \)

d. \( \scriptsize 7n^{\frac{7}{2}}\)

Answers

a. 15

b. \( \scriptsize 4^4\)

c. \( \scriptsize 3^{5} \)

d. \( \scriptsize12^4\)

e. \(\scriptsize 4y^9 \)

f. \( \scriptsize 5d^7 \)

g. \( \frac{1}{2} x^2 \)

h. \( \frac{1}{4} d^3 \)

Answers

a. \( \frac{1}{10^5}\)

b. \( \frac{1}{7^3}\)

c. \( \frac{1}{9^2}\)

d. \( \frac{1}{x^2}\)

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

f. \( \frac{1}{10^3}\)

Answers

a. \( \frac{20b}{a^3}\)

b. \( \frac{1}{49x^2}\)

c. \( \frac{5}{a^4}\)

d. \( \frac{1}{2}\)

e. \(\scriptsize 8 \)

f. \( \frac{1}{2g}\)

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