Numbers with exponents

Numbers with exponents

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This task is about solving maths problems with exponents.

Some students were giving answers to maths problems written with exponent notation. 

Identify which student is correct and explain why. Do NOT use a calculator in this problem.

Question

a)

 

 "What is 56 × 53?"

  • Awhina said "It equals 259".
  • Rosa said "It equals 56".
  • Karaka said "It equals 59".
  • Hari said "It equals 518".
  • Sarah said "None of your answers are right".
     Which student is correct?

    • Awhina

    • Rosa

    • Karaka

    • Hari

    • Sarah

Explain your answer

Question

b)

 

 "What is 78 ÷ 72?"

  • Awhina said "It equals 74".
  • Rosa said "It equals 76".
  • Karaka said "It equals 710".
  • Hari said "It equals 716".
  • Sarah said "None of your answers are right".
Which student is correct?

    • Awhina

    • Rosa

    • Karaka

    • Hari

    • Sarah

Explain your answer

Question

c)

 

 "What is 26 × 43?"

  • Awhina said "It equals 86".
  • Rosa said "It equals 69".
  • Karaka said "It equals 818".
  • Hari said "It equals 212".
  • Sarah said "It equals 618".
Which student is correct?

    • Awhina

    • Rosa

    • Karaka

    • Hari

    • Sarah

Explain your answer
Task administration: 
This task can be completed with pencil and paper or online (with SOME auto marking).
Students should NOT use a calculator in this problem.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Strategies
Keywords: 
index form, exponents, indices, powers, multiplication, division
Description of task: 
Students select which person has correctly applied the laws of indices to some problems, and explain their choice.
Answers/responses: 
    Y10 (03/2004)
a) i) Karaka [Accept 59]
ii) Explanation based on any 1 of:

  • When you multiply you add the indices;
  • 56 = 5 × 5 × 5 × 5 × 5 × 5 and 53 = 5 × 5 × 5,
    so 56 × 53 = 5 × 5 × ... × 5 = 59;
  • other reasonable explanations
 moderate 
moderate
b) i) Rosa [Accept 76]
ii) Explanation based on any 1 of:

  • When you divide you subtract the indices;
  • 78 = 7 × 7 × ... × 7 and 72 = 7 × 7 and 7 ÷ 7 = 1,
    so 78 ÷ 72 = 7 × 7 × ... × 7 = 76;
  • other reasonable explanations
 moderate 
difficult
c) i) Hari [Accept 212 or None and 46]
ii) For any 1 of:

  • 26 = 2 × 2 × 2 × 2 × 2 × 2 and
    43 = (2 × 2)3 = 2 × 2 × 2 × 2 × 2 × 2,
    26 × 43 = 2 × 2 × ... × 2 = 212;
  • 43 = 64 = 26; 26 × 26 = 212;
  • 43 = (22)3 = 26; 26 × 26 = 212;
  • 26 = 43; 43 × 43 = 46; (= 212);
  • other reasonable explanations.
 difficult 
very difficult

NOTE: Do not accept exact calculations, e.g., they both equal 1 953 125, 117 649, or 4 096.