Indices

Indices, SMB-032

Rationalise the denominator of the surd fraction . (3 marks)

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Indices, SMB-031

Rationalise the denominator of the surd fraction . (3 marks)

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Indices, SMB-029

Expand and simplify . (2 marks)

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Indices, SMB-028

Expand and simplify . (2 marks)

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Indices, SMB-075

Simplify . (2 marks)

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Indices, SMB-030

Find the reciprocal of . (3 marks)

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Indices, SMB-027

Simplify . (2 marks)

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Indices, SMB-026

Find and such that are real numbers and

. (2 marks)

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Indices, SMB-025

Show working to find and such that are real numbers and

. (2 marks)

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Indices, SMB-024

Show working to simplify and such that are real numbers and

. (2 marks)

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Indices, SMB-023

Rationalise the denominator of . (2 marks)

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Indices, SMB-022

Simplify and express as a fraction involving non-negative indices only. (3 marks)

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Indices, SMB-021

Simplify and express as a fraction involving non-negative indices only. (3 marks)

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Indices, SMB-020

Express as a fraction involving non-negative indices only. (1 mark)

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Indices, SMB-019

Express as a fraction involving non-negative indices only. (1 mark)

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Indices, SMB-018

Simplify the expression . (1 mark)

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Indices, SMB-017

Simplify the expression . (1 mark)

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Indices, SMB-016

Simplify the expression . (1 mark)

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Indices, SMB-015

Simplify the expression . (1 mark)

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Indices, SMB-014

Express as a fraction. (1 mark)

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Indices, SMB-013

Simplify the expression . (2 marks)

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Indices, SMB-012

Simplify the expression . (2 marks)

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Indices, SMB-011

Simplify the expression . (2 marks)

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Indices, SMB-010

Simplify the expression . (2 marks)

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Indices, SMB-009

Find given . (2 marks)

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Indices, SMB-008

Solve the equation for . (2 marks)

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Indices, SMB-007

Solve the equation for (2 marks)

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Indices, SMB-006 MC

Select the expression that is equivalent to

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Indices, SMB-005 MC

Which of the following has the same value as

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Indices, SMB-004 MC

Which expression is equal to ?

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Indices, SMB-003 MC

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Inices, SMB-002 MC

is equal to which of the following?

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Indices, SMB-001 MC

Which of the following is equal to 32?

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L&E, 2ADV E1 2019 HSC 3 MC

What is the value of so that ?

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Algebra, 2UG 2016 HSC 26b

Simplify . (2 marks)

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Algebra, 2UG 2015 HSC 11 MC

Which of the following is in its simplest form?

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♦ Mean mark below 43%. BE CAREFUL!

Algebra, 2UG 2006 HSC 23a

Simplify (2 marks)

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Functions, 2ADV F1 2004 HSC 1d

Find integers and by showing working to expand and simplify

. (2 marks)

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Algebra, 2UG 2005 HSC 7 MC

Simplify

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Algebra, 2UG 2008 HSC 1 MC

Which expression is equivalent to ?

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Functions, 2ADV F1 2008 HSC 1e

Expand and simplify . (2 marks)

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Algebra, 2UG 2014 HSC 11 MC

Simplify .

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Algebra, 2UG 2010 HSC 27a

Fully simplify . (3 marks)

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♦♦ Mean mark 33%.
MARKER’S COMMENT: Remember to “invert and multiply” when dividing a fraction by a fraction (see Worked Solution).

Algebra, 2UG 2012 HSC 28b

Simplify fully . (2 marks)

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♦ Mean mark 35%!

Algebra, 2UG 2011 HSC 12 MC

Which of the following expresses in its simplest form?

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ALGEBRA TIP: When you divide by a fraction, invert the divisor and multiply as shown in the Worked Solution.

Algebra, 2UG 2013 HSC 5 MC

Which of the following is in its simplest form?

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L&E, 2ADV E1 2011 HSC 1c

Solve . (2 marks)

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MARKER’S COMMENT: Many students correctly solved this by taking the logarithms of both sides.