Junior Cycle Mathematics Indices: Fill in the table by writing eac

Fill in the table by writing each expression in the form $2^p$, where $p \in \mathbb{N}$ - Junior Cycle Mathematics - Question 11 - 2016

Question 11

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Fill in the table by writing each expression in the form $2^p$, where $p \in \mathbb{N}$. One has already been filled in for you. Expression 8 = 32 = $2 \times 2... show full transcript

Worked Solution & Example Answer:Fill in the table by writing each expression in the form $2^p$, where $p \in \mathbb{N}$ - Junior Cycle Mathematics - Question 11 - 2016

Step 1

8 =

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Answer

The number 8 can be expressed as powers of 2. We can write:

$8 = 2 \times 2 \times 2 = 2^3$

Step 2

32 =

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Answer

The number 32 can also be expressed as powers of 2. It is equal to:

$32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5$

Step 3

2 \times 2 \times 2 \times 2 \times 2 \times 2 =

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Answer

This expression contains six factors of 2. Therefore, we can write:

$2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^6$

Step 4

2^7 \times 2^{10} =

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Answer

According to the laws of exponents, when we multiply the same base, we add the exponents. Thus:

$2^7 \times 2^{10} = 2^{7 + 10} = 2^{17}$

Step 5

(2^6)^4 =

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Answer

Using the power of a power rule (which states that $(a^m)^n = a^{mn}$ ), we get:

$\left(2^6 \right)^4 = 2^{6 \times 4} = 2^{24}$

Fill in the table by writing each expression in the form $2^p$, where $p \in \mathbb{N}$ - Junior Cycle Mathematics - Question 11 - 2016

Worked Solution & Example Answer:Fill in the table by writing each expression in the form $2^p$, where $p \in \mathbb{N}$ - Junior Cycle Mathematics - Question 11 - 2016

8 =

32 =

2 \times 2 \times 2 \times 2 \times 2 \times 2 =

2^7 \times 2^{10} =

(2^6)^4 =

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