SS1: MATHEMATICS - 1ST TERM
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Number Base System I6 Topics|2 Quizzes
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Number Base System II3 Topics
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Number Base System III2 Topics|1 Quiz
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Modular Arithmetic I2 Topics
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Modular Arithmetic II3 Topics
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Modular Arithmetic III4 Topics|1 Quiz
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Indices I3 Topics|1 Quiz
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Indices II1 Topic|1 Quiz
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Logarithms I3 Topics
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Logarithms II4 Topics|1 Quiz
Worked Examples – Indices 1
Topic Content:
- Worked Examples – Indices 1
Try to work these examples out on your own using the laws of indices.
Check the solutions by clicking (“View Solution”)
Worked Examples 7.3.1:
Evaluate the following:
(a) \( \scriptsize 5x^{-2}y \:\times\: 2x ^{-5}y^2\)
SOLUTION (a)
Question
⇒ \(\scriptsize 5x^{-2}y \times 2x ^{-5}y^2\)
Solution
Group like terms together
⇒ \(\scriptsize 5x^{-2} \times 2x ^{-5} \times y \times y^2\)
From the Laws of Indicies \(\scriptsize X^a \times X^b = X^{a + b}\)
∴ \(\scriptsize 10x^{-2 + (-5)} \times y^{1 + 2}\)
= \(\scriptsize 10x^{-7} \times y^{3}\)
From the Laws of Indicies \(\scriptsize X^{-a} = \normalsize \frac {1}{X^a}\)
∴ \(\scriptsize x^{-7} = \normalsize \frac{1}{x^{7}}\)
∴ \(\scriptsize 10\: \times \: \normalsize \frac{1}{x^{7}} \scriptsize \: \times \: y^{3}\\ = \normalsize \frac{10y^3}{x^{7}}\)
(b) \( \scriptsize 2^{4}\: \times \: \normalsize \left(\frac {1}{8}\right)^{^{-1} } \scriptsize \: \times \: 4^0\)
SOLUTION (b)
Question
⇒ \(\scriptsize 2^{4} \: \times \: \normalsize\left (\frac {1}{8}\right )^{^{-1}} \scriptsize \: \times \: 4^0\)
Solution
From the Laws of Indicies \(\scriptsize X^0 = 1 \scriptsize \; and \; X^{-a} = \normalsize \frac {1}{X^a}\)
∴ \(\scriptsize 4^0 = 1 \: and \: \normalsize \left( \frac {1}{8}\right)^{^{-1}} = \left(\frac {8}{1}\right)^{^{1}} \scriptsize = 8\)
⇒ \(\scriptsize 2^{4} \times \normalsize \left(\frac {1}{8}\right)^{^{-1}} \scriptsize \times 4^0\)
= \(\scriptsize 2^{4} \times \scriptsize 8 \times 1\)
Note: 8 = 2 x 2 x 2 = \(\scriptsize 2^3\)
∴ = \(\scriptsize 2^{4} \times 2^{3}\)
From the Laws of Indicies \(\scriptsize X^a \:\times \: X^b = X^{a + b}\)
∴ \(\scriptsize 2^{4+ 3} = 2^7 \: or \: 128\)
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