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Exercise 1a (Chapter 1: Indices and Logarithms)

Here, we have answered all the questions contained in exercise 1a of the New General Mathematics for SS1. Feel free to ask your questions if you do not understand so we can give you proper explanations regarding each of the steps we took.

Exercise 1a (Revision)

Instruction: Simplify the following

Question 1:

$10^{5} \times 10^{4}$

$10^{5} \times 10^{4}$

$=10^{5+4}$

$=10^{9}$

Question 2:

$a^{3}\times a^{9}$

$a^{3}\times a^{9}$

$a^{3+9}$

$a^{12}$

Question 3:

$5y \times 4y^{4}$

$5y \times 4y^{4}$

$=(5\times 4) \times (y\times y^{4})$

$=20 \times y^{1+4}$

$=20 \times y^{5}$

$= 20y^{5}$

Question 4:

$2^{2} \times 2^{4}$

$2^{2}\times 2^{4}$

$=2^{2+4}$

$=2^{6}$

$=64$

Question 5:

$m^{8} \div m^{5}$

$m^{8} \div m^{5}$

$m^{8-5}$

$m^{3}$

Question 6:

$c^{7} \div c$

$c^{7} \div c$

$c^{7-1}$

$c^{6}$

Question 7:

$24x^{6} \div 8x^{4}$

$\frac {24x^{6}}{8x^{6}}$

$(\frac{24}{8})\times(\frac{x^{6}}{x^{4}})$

$=3\times x^{6-4}$

$=3 \times x^{2}$

$= 3x^{2}$

Question 8:

$\frac {9\times 10^{9}}{3 \times 10^{3}}$

$\frac {9\times 10^{9}}{3 \times 10^{3}}$

$=(\frac{9}{3}) \times (\frac{10^{9}}{10^{3}})$

$=3 \times (10^{9-3})$

$=3\times 10^{6}$

Question 9:

$2^{0}$

$2^{0}$

Anything to the power of zero is 1

$\therefore 2^{0} = 1$

Question 10:

$6 \times z^{0}$

$6 \times z^{0}$

Anything to the power of zero is 1

$z^{0}=1$

$\therefore 6 \times z^{0}=6\times 1 = 6$

Question 11:

$4^{-3}$

$4^{-3}$

$=\frac{1}{4^{3}}$

$=\frac{1}{64}$

Question 12:

$3x^{-3}$

$3x^{-3}$

$= 3 \times x^{-3}$

$= 3 \times \frac{1}{x^{3}}$

$= \frac {3}{x^{3}}$

Question 13:

$(1-4)^{-2}$

$(1-4)^{-2}$

$=(-3)^{-2}$

$= \frac{1}{(-3)^{2}}$

$= \frac{1}{9}$

NOTE: The answer 16 as shown at the answer page of the New General Mathematics for SSS 1 textbook is not correct.

Question 14:

$(2-3)^{-1}$

$(2-3)^{-1}$

$= (-1)^{-1}$

$= \frac{1}{-1}$

$= -1$

NOTE: The answer shown at the answer page of the New General Mathematics for SS1 is not correct.

Question 15:

$x^{3} \div x^{-5}$

$x^{3} \div x^{-5}$

$=x^{3-(-5)}$

$=x^{3+5}$

$=x^{8}$

Question 16:

$a^{-9}\div b^{0}$

$a^{-9}\div b^{0}$

Anything to the power of zero is 1

$=a^{-9}\div 1$

$=\frac {1}{a^{9}} \div 1$

$=\frac{\frac{1}{a^{9}}}{1}$

$=\frac{1}{a^{9}}$ or $a^{-9}$

Question 17:

$(3x)^{-3}$

$(3x)^{-3}$

$=\frac{1}{(3x)^{3}}$

$=\frac{1}{(3\times x)^{3}}$

$=\frac{1}{3^{3}\times x^{3}}$

$=\frac{1}{27 \times x^{3}}$

$=\frac{1}{27x^{3}}$

Question 18:

$9a^{-5} \times 4a^{6}$

$9a^{-5} \times 4a^{6}$

$= (9\times4)\times (a^{-5} \times a^{6})$

$= 36 \times a^{-5+6}$

$= 36 \times a$

$=36a$

Question 19:

$5x^{2} \times 4x^{0} \times 2x^{-6}$

$5x^{2} \times 4x^{0} \times 2x^{-6}$

$= (5\times 4 \times 2) \times (x^{2} \times x^{0} \times x^{-6})$ latex = 40 \times (x^{2+0+(-6)}&s=2$

$=40 \times x^{-4}$

$= 40x^{-4}$

OR

$= 40 \times \frac{1}{x^{4}}$

$=\frac{40}{x^{4}}$

Question 20:

$15 \times 10^{4} \div (3\times 10^{-2})$

$15 \times 10^{4} \div (3\times 10^{-2})$

$= \frac{15 \times 10^{4}}{3 \times 10^{-2}}$

$= (\frac{15}{3}) \times (\frac{10^{4}}{10^{-2}})$

$= 5 \times 10^{4-(-2)}$

$= 5 \times 10^{4+2}$

$= 5 \times 10^{6}$

$= 5 000 000$

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