Content description VC2M9A01

Mathematics Version 2.0 / Level 9 / Algebra

Content description

apply the exponent laws to numerical expressions with integer exponents and the zero exponent, and extend to variables

Elaborations

representing decimals in exponential form; for example, 0.475 can be represented as $0.475 = \frac{4}{10} + \frac{7}{100} + \frac{5}{1000} = 4 \times 10^{- 1} + 7 \times 10^{- 2} + 5 \times 10^{- 3}$ and 0.00023 as 23 × 10^-5
simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, $5^{- 3} = \frac{1}{5^{3}} = {(\frac{1}{5})}^{3} = \frac{1}{125}$ and connecting terms of the sequence $125, 25, 5, 1, \frac{1}{5}, \frac{1}{25}, \frac{1}{125}$ … to terms of the sequence $5^{3}, 5^{2}, 5^{1}, 5^{0}, 5^{- 1}, 5^{- 2}, 5^{- 3}$ ...
relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, $2^{3} \div 2^{5} = 2^{- 2} = \frac{1}{2^{2}} = \frac{1}{4}$ and ${(3 \times 5)}^{2} = 3^{2} \times 5^{2} = 9 \times 25 = 225$
recognising exponents in algebraic expressions and applying the relevant exponent laws and conventions; for example, for any non-zero natural number $a$ , $a^{0} = 1$ , $x^{1} = x, {r^{2} = r \times r, h}^{3} = h \times h \times h,$ $y^{4} = y \times y \times y \times y$ , and $\frac{1}{w} \times \frac{1}{w} = \frac{1}{w^{2}} = w^{- 2}$
relating simplification of expressions from first principles and counting to the use of exponent laws; for example,
${(a^{2})}^{3} = (a \times a) \times (a \times a) \times (a \times a) = a \times a \times a \times a \times a \times a = a^{6}$ ;
$b^{2} \times b^{3} = (b \times b) \times (b \times b \times b) = b \times b \times b \times b \times b = b^{5}; \frac{y^{4}}{y^{2}} = \frac{y \times y \times y \times y}{y \times y} = \frac{y^{2}}{1} = y^{2}$ and ${(5 a)}^{2} = (5 \times a) \times (5 \times a) = 5 \times 5 \times a \times a = 25 \times a^{2} = 25 a^{2}$
applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, $\frac{{(2 x y)}^{3}}{{x y}^{4}} = \frac{8 x^{3} y^{3}}{x y^{4}} = 8 x^{2} y^{- 1}$
relating the prefixes for SI units from pico- (trillionth) to tera- (trillion) to the corresponding powers of 10; for example, one pico-gram = 10^-12grams and one terabyte = 10¹² bytes

Code

VC2M9A01

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