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Indices, SM-Bank 039

  1. Explain why a negative number raised to an odd power will always have a negative answer.  (2 marks)

  2. Give 2 worked examples that verify your explanation.  (2 marks)

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a.    \(\text{See worked solution}\)

b.    \(\text{See worked solution}\)

Show Worked Solution

a.    \(\text{A negative number multiplied by a negative}\)

\(\text{number an odd number of times always a has}\)

\(\text{negative answer.}\)

\(\text{It therefore, follows that when a negative number}\)

\(\text{is raised to an odd power, such as 1, 3, 5…, }\)

\(\text{the answer is also always negative.}\)

\(\text{ie } (-\times -)\times – =+\times -=-\)

b.    \(\text{Examples (Others are also acceptable)}\)

\((-1)^3=(-1\times -1)\times -1=1\times -1=-1\)

\((-1)^5=(-1\times -1)\times (-1\times -1)\times -1=1\times 1\times -1=-1\)

Indices, SM-Bank 038

  1. Explain why a negative number raised to an even power will always have a positive answer.  (2 marks)

  2. Give 2 worked examples that verify your explanation.  (2 marks)

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a.    \(\text{See worked solution}\)

b.    \(\text{See worked solution}\)

Show Worked Solution

a.    \(\text{A negative number multiplied by a negative}\)

\(\text{number always a has positive answer.}\)

\(\text{It therefore, follows that when a negative number}\)

\(\text{is multiplied by a negative number, an even}\)

\(\text{number of times, as is the case with even powers}\)

\(\text{such as 2, 4, 6…, the answer is also always positive.}\)

b.    \(\text{Examples (Others are also acceptable)}\)

\((-1)^2=-1\times -1=1\)

\((-1)^4=-1\times -1\times -1\times -1=1\)

Indices, SM-Bank 034

Evaluate \(2^2\times 7-5\times 4^3\).  (2 marks)

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\(-292\)

Show Worked Solution
\(2^2\times 7-5\times 4^3\) \(=(2\times 2)\times 7-5\times (4\times 4\times 4)\)
  \(=4\times 7-5\times 64\)
  \(=28-320=-292\)

Indices, SM-Bank 015 MC

Which expression is equal to  \(6^3\times 36^2\)?

  1. \(6\times 3\times 36\times 2\)
  2. \(6\times 6\times 6\times 6\times 6\)
  3. \(6\times 6\times 6\times 36\times 6\)
  4. \(6\times 6\times 6\times 6\times 6\times 6\times 6\)
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\(D\)

Show Worked Solution
\(6^3\times 36^2\) \(= (6\times 6\times 6)\times (6\times 6)^2\)
  \(= (6\times 6\times 6) \times (6\times 6)\times (6\times 6)\)
  \(=6\times 6\times 6\times 6\times 6\times 6\times 6\)

 
\(\Rightarrow D\)

Indices, SM-Bank 014 MC

\(2^5-2^3 =\)
 

Which number makes the expression above correct?

  1. \(4\)
  2. \(8\)
  3. \(24\)
  4. \(28\)
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\(C\)

Show Worked Solution
\(2^5-2^3\) \(=2\times 2\times 2\times 2\times 2-2\times 2\times 2\)
  \(=32-8\)
  \(=24\)

 
\(\Rightarrow C\)

Indices, SM-Bank 012 MC

\(30^2\) is equal to which of the following?

  1. \(60^2÷3\)
  2. \(3^2\times 2\times 5\times 2\times 5\)
  3. \(9\times 5^2\)
  4. \(3\times 10\times 10\)
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\(B\)

Show Worked Solution

\(30^2=900\)

\(\text{Checking Option B:}\)

\(3^2\times 2\times 5\times 2\times 5\)

\(= 3^2\times 10\times 10\)

\(=900\)

 
\(\Rightarrow B\)

Indices, SM-Bank 010 MC

Which one of these has the same value as \(16^2\)? 

  1. \(32^2\ ÷\ 4\)
  2. \(2\times 2\times 4\times 2\times 4\)
  3. \(2\times 8^2\)
  4. \(2\times 16\times 16\)
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\(A\)

Show Worked Solution
\(16^2\) \(=16\times 16\)
  \(=32\ ÷\ 2\times 32\ ÷\ 2\)
  \(=32^2\ ÷\ 4\)

 
\(\Rightarrow A\)