law of indices question

Alternative transcript:

an expression in the form ab+c as a¹ × ac. [Edexcel GCSE June2003-6H Q17ai] x = 2P, y = 29 Express 2P+q in terms of x and/or y. Question 9 Categorisation: As above, but with the law ab ÷ ac = ab-c [Edexcel GCSE June2003-6H Q17aiii] x = 2P, y = 29 Express 2P-1 in terms of x and/or y . Question 10 Categorisation: Recognise that abc could be written as either (ab) or (aº)¹. [Edexcel GCSE June2003-6H Q17aii] x = 2P, y = 29 Express 229 in terms of x and/or y. www.drfrostmaths.com Question 11 Categorisation: Identify a missing power when negative indices are involved. [Edexcel GCSE Nov2011-3H Q18b] Write down the value of y. [Edexcel GCSE June2003-31 Q24iii] Work out the value of 2y = 4 Question 12 Categorisation: Combine laws of indices with laws of surds, in particular recognizing that √a² = (a¹)² = azº, i.e. square rooting has the effect of halving the power. 24 x 9 www.drfrostmaths.com Question 13 Categorisation: As above, but with other roots (e.g. cube root) and where prior simplification may be required. [Edexcel GCSE(9-1) Mock Set 2 Spring 2017 1H Q15a] Find the value of y = √27 x 3 x 108 Question 14 Categorisation: Recognise that a square root can be written using a power of thus enabling the entire term to be written as a power, e.g. 25√√5 = 5² × 52 = 52. 5 [Edexcel GCSE June2006-5H Q20b] 8√8 can be written in the form 8k Find the value of k. Question 15 Categorisation: As above but a more complex mixture of terms. [Edexcel IGCSE Jan2016(R)-3H Q13b] Work out the value of k. និ www.drfrostmaths.com √√√a² k = ak k = Question 16 Categorisation: Use laws of indices to multiply algebraic terms. [Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 3H Q10] Simplify 3m²r x 4m³r6 Question 17 Categorisation: Use laws of indices to divide algebraic terms. [Edexcel IGCSE Jan2016-3H Q4d] Expand and simplify 36k³m4 30k5m Question 18 Categorisation: Raise a single term to a power. [Edexcel IGCSE Jan2016(R)-3H Q13a] Simplify (4h) ³ Question 19 Categorisation: Raise a single term to a fractional power. [Edexcel GCSE June2010-4H Q22d] Simplify (9w²y6) www.drfrostmaths.com Question 20 Categorisation: Change all terms to a consistent base where they are different, e.g. 9x × 3² = (32)* × 3² = 3²x × 3² = 32x+2 [Edexcel GCSE Nov2007-5H Q16b] Work out the value of x. Question 21 Categorisation: Recognise that (ab) = (ac)b 2308⁹ = 2x [Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 - 2H Q14] Given that 3-" = 0.2, find the value of (34)" Write down the value of Question 22 Categorisation: Raise a number to a fractional power with denominator 1. [Edexcel GCSE June2006-5H Q20a] www.drfrostmaths.com X = Question 23 Categorisation: Raise a number to any (positive) fraction. [Edexcel GCSE June2003-5H Q16iii] Work out 162 Question 24 Categorisation: Raise a number to a negative integer power. [Edexcel GCSE June2003-5H Q16ii] Work out 4-2 Question 25 Categorisation: Raise a number to a negative an fractional power. [Edexcel GCSE(9-1) Mock Set 1 Autumn 2016-1H Q10] Find the value of 64 3 Question 26 Categorisation: Raise a fraction to a power. [Edexcel GCSE June 2010-3H Q24iii] (²7) ³. Find the value of www.drfrostmaths.com Question 27 Categorisation: As above, but where the fraction can first be simplified. [Edexcel GCSE(9-1) Mock Set 2 Spring 2017 1H Q15b] Find the value of 216\/ Question 28 Categorisation: Raise a fraction involving algebraic terms to a negative power. [Edexcel GCSE Nov2014-1H Q22b] Simplify www.drfrostmaths.com 64x6) 25y² Question 29 Categorisation: Raise a fraction involving algebraic terms to a positive power. [Edexcel IGCSE Jan2016-4H Q17a] Simplify -=-=- 8e6\ f12 ³ Question 30 Categorisation: Use laws of indices in the context of simultaneous equations. [Edexcel GCSE June2003-6H Q17b] x = 2P, y = 29 xy = 32 and 2xy² = 32 Find the value of p and the value of q. Question 31 Categorisation: Order numbers each raised to a power. [Edexcel GCSE June2010-4H Q22e] For x > 1, write the following expressions in order of size: 구를 xo www.drfrostmaths.com x² X x-2 Question 32 Categorisation: Use laws of indices in the context of standard form. [Edexcel IGCSE Jan2016-4H Q25] y = 16 x 108k where k is an integer. Find an expression, in terms of k, for y Give your answer in standard form. Answers Question 1 64 Question 2 Question 3 Question 4 Question 5 ITT Question 6 Question 7 Question 8 xy Question 9 플 Question 10 y² Question 11 y = -2 www.drfrostmaths.com Question 12 12 Question 13 300 Question 14 k = 1.5 Question 15 k = ³/6 Question 16 12m5r7 Question 17 6m³ 5k² Question 18 64h² Question 19 3wy³ Question 20 x = 3 Question 21 625 Question 22 2 Question 23 64 www.drfrostmaths.com Question 24 16 Question 25 1 16 Question 26 4 Question 27 25 9 Question 28 5y 8x3 Question 29 2e² f4 Question 30 p=6, q = -1 Question 31 x-², x⁰, x², x,x² Question 32 www.drfrostmaths.com 3.2 x 1010k+1