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=410+7100+51000=4×10-1+7×10-2+5×10-3 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=153=(15)3=1125 and connecting terms of the sequence 125,25,5,1,15,125,1125… to terms of the sequence 53,52,51,50,5-1,5-2,5-3...
relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, 23÷25=2-2=122=14and (3×5)2=32×52=9×25=225
recognising exponents in algebraic expressions and applying the relevant exponent laws and conventions; for example, for any non-zero natural number a, a0=1, x1=x,r2=r×r,h3=h×h×h,y4=y×y×y×y, and1w×1w=1w2=w-2
relating simplification of expressions from first principles and counting to the use of exponent laws; for example, (a2)3=a×a×a×a×a×a=a×a×a×a×a×a=a6; b2×b3=b×b×b×b×b=b×b×b×b×b=b5;y4y2=y×y×y×yy×y=y21=y2and(5a)2=5×a×5×a=5×5×a×a=25×a2=25a2
applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, (2xy)3xy4=8x3y3xy4=8x2y-1
relating the prefixes for SI units from pico- (trillionth) to tera- (trillion) to the corresponding powers of 10; for example, one pico-gram = 10-12 grams and one terabyte = 1012 bytes
Code
VC2M9A01
Curriculum resources and support
Find related teaching and learning resources in
Arc*
