The table below shows the values when 3 is raised to certain powers. (i) Complete the table. Power of 3 | Expanded power of 3 | Answer ------------|------------------------|------- $3^1$ | $3$ | $3$ $3^2$ | $3 \times 3$ | $9$ $3^3$ | $3 \times 3 \times 3$ | $27$ $3^4$ | $3 \times 3 \times 3 \times 3$ | $81$ $3^5$ | $3 \times 3 \times 3 \times 3 \times 3$ | $243$ (ii) $3^3$ is 6561. Explain how you could use this to find the value of $3^3$ without using a calculator.

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The table below shows the values when 3 is raised to certain powers - Junior Cycle Mathematics - Question 4 - 2014

Question 4

The table below shows the values when 3 is raised to certain powers. (i) Complete the table. Power of 3 | Expanded power of 3 | Answer ------------|------------... show full transcript

Worked Solution & Example Answer:The table below shows the values when 3 is raised to certain powers - Junior Cycle Mathematics - Question 4 - 2014

Step 1

Complete the table:

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Answer

For $3^1$ , the expanded power is $3$ and the answer is $3$ .
For $3^2$ , the expanded power is $3 \times 3$ and the answer is $9$ .
For $3^3$ , the expanded power is $3 \times 3 \times 3$ and the answer is $27$ .
For $3^4$ , the expanded power is $3 \times 3 \times 3 \times 3$ and the answer is $81$ .
For $3^5$ , the expanded power is $3 \times 3 \times 3 \times 3 \times 3$ and the answer is $243$ .

Step 2

Explain how you could use this to find the value of $3^3$ without using a calculator:

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Answer

Since $3^3$ equals $6561$ , you can multiply this value by $3$ to find the next power, $3^4$ : $3^4 = 3 \times 3^3 = 3 \times 6561 = 19683.$ Alternatively, you can express it as $3 \times 3^2 = 3^1 \times 3^3 = 3^{1+3} = 3^4$ .

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