smc-4214-12-Index form

Indices, SM-Bank 029

Write 625 in:

Expanded form. (1 mark)

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Index form. (1 mark)

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a. \(5\times 5\times 5\times 5\)

b. \(5^4\)

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a.	\(625\)	\(=5\times 125\)
		\(=5\times (5\times 25)\)
		\(=5\times 5\times 5\times 5\)

b. \(625=5^4\)

Indices, SM-Bank 028

Write \(100\ 000\) in:

Expanded form. (1 mark)

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Index form. (1 mark)

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a. \(10 \times 10 \times 10 \times 10 \times 10\)

b. \(10^5\)

Show Worked Solution

a. \(100\ 000=10\times 10 \times 10 \times 10 \times 10\)

b. \(100\ 000=10^5\)

Indices, SM-Bank 027

Write \(1\ 000\ 000\) in:

Expanded form. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
Index form. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

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a. \(10 \times 10 \times 10 \times 10 \times 10 \times 10\)

b. \(10^6\)

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a. \(1\ 000\ 000=10\times 10 \times 10 \times 10 \times 10 \times 10\)

b. \(1\ 000\ 000=10^6\)

Indices, SM-Bank 025

Express 16 as a power of 2. (1 mark)

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\(2^4\)

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\(16\)	\(=4\times 4\)
	\(=(2\times 2)\times (2\times 2)\)
	\(=2^4\)

Indices, SM-Bank 024

Express 32 as a power of 2. (2 marks)

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\(2^5\)

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\(32\)	\(=2\times 16\)
	\(=2\times (4\times 4)\)
	\(=2\times (2\times 2)\times (2\times 2)\)
	\(=2^5\)

Indices, SM-Bank 023

Insert the index powers that make this statement correct. (2 marks)

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\(3\text{ and }2\)

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\(108\)	\(=12\times 9\)
	\(=(4\times 3)\times (3\times 3)\)
	\(=(2\times 2\times 3)\times (3\times 3)\)
	\(=3^3\times 2^2\)

\(\therefore\ \text{The correct powers are }3\text{ and }2.\)

Indices, SM-Bank 022

Insert the index powers that make this statement correct. (2 marks)

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\(2\text{ and }4\)

Show Worked Solution

\(144\)	\(=12\times 12\)
	\(=(4\times 3)\times (4\times 3)\)
	\(=(2\times 2\times 3)\times (2\times 2\times 3)\)
	\(=3^2\times 2^4\)

\(\therefore\ \text{The correct powers are }2\text{ and }4.\)

Indices, SM-Bank 021

Insert the index power that makes this statement correct. (2 marks)

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\(4\)

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\(81\)	\(=9\times 9\)
	\(=(3\times 3)\times (3\times 3)\)
	\(=3^4\)

\(\therefore\ \text{The correct power is}\ 4\)

Indices, SM-Bank 020

Write \(7\times 3\times 5\times 5\times 7\times 7\times 5\times 5\times 5\) in index form. (2 marks)

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\(7^3\times 5^5\times 3^1\)

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\(7\times 3\times 5\times 5\times 7\times 7\times 5\times 5\times 5\)

\(=7^3\times 5^5\times 3^1\)

Indices, SM-Bank 019

Write \(4\times 3\times 4\times 4\times 3\) in index form. (2 marks)

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\(4^3\times 3^2\)

Show Worked Solution

\(4\times 3\times 4\times 4\times 3\)

\(=4^3\times 3^2\)

Indices, SM-Bank 018

Write \(3\times 3\times 3\times 2\times 2\) in index form. (2 marks)

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

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\(3\times 3\times 3\times 2\times 2\)

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