Express `4^(-3)` as a fraction. (1 mark)
Indices, SMB-013
Simplify the expression `36t^7 -: 27t^3`. (2 marks)
Indices, SMB-012
Simplify the expression `24a^8 -: 3a^2`. (2 marks)
Indices, SMB-011
Simplify the expression `(5p^3)^2`. (2 marks)
Indices, SMB-010
Simplify the expression `(2x^3)^4`. (2 marks)
Indices, SMB-009
Find `x` given `100^(x-2) = 1000^x`. (2 marks)
Indices, SMB-008
Solve the equation `2^(3x-3) = 8^(2-x)` for `x`. (2 marks)
Indices, SMB-007
Solve the equation `3^(-4x) = 9^(6-x)` for `x.` (2 marks)
Indices, SMB-006 MC
Select the expression that is equivalent to `(4^(-3) ÷ 4^6)^3`
- `4^(-27)`
- `4^(-9)`
- `4^(-54)`
- `4^(-6)`
Indices, SMB-005 MC
Which of the following has the same value as `7^(-11)?`
- `-7^(-11)`
- `7 xx (-11)`
- `1/-7^11`
- `1/7^11`
Indices, SMB-004 MC
Which expression is equal to `6^3 xx 36^2`?
- `6 xx 3 xx 36 xx 2`
- `6 xx 6 xx 6 xx 6 xx 6`
- `6 xx 6 xx 6 xx 36 xx 6`
- `6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`
Indices, SMB-003 MC
`7 xx 2^3 =`
- `28`
- `42`
- `56`
- `2744`
Inices, SMB-002 MC
`30^2` is equal to which of the following?
- `60^2 ÷ 3`
- `3^2 xx 2 xx 5 xx 2 xx 5`
- `9 xx 5^2`
- `3 xx 10 xx 10`
Indices, SMB-001 MC
Which of the following is equal to 32?
- `2^3 xx 2^2`
- `2^3 + 2^2`
- `3^2 + 2^2`
- `3^2 xx 2^2`
Algebraic Techniques, SMB-071
Simplify the expression `4/(y^2-16)+1/(3y-12)` (3 marks)
Algebraic Techniques, SMB-070
Simplify the expression `(5a-15)/3xx(6a)/(a^2-9)` (3 marks)
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Algebraic Techniques, SMB-069
Factorise the expression `5/(x^2-1)-3/(x-1)` (3 marks)
Algebraic Techniques, SMB-068
Factorise the expression `5/(b^2-b)-2/(b^2-1)` (3 marks)
Algebraic Techniques, SMB-067
Factorise the expression `(x^2-7x+12)/(x-3)` (2 marks)
Algebraic Techniques, SMB-066
Factorise the expression `-12y^2+18y-6` (2 marks)
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Algebraic Techniques, SMB-065
Fully factorise the expression `6y^2+10y-4` (2 marks)
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Algebraic Techniques, SMB-064
Factorise the expression `2x^2+x-6` (2 marks)
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Algebraic Techniques, SMB-063
Fully factorise the expression `3a^2+12ab-2a-8b` (2 marks)
Algebraic Techniques, SMB-062
Fully factorise the expression `2x^2-6xy-3x+9y` (2 marks)
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Algebraic Techniques, SMB-061
Factorise the expression `5b^3-5b` (2 marks)
Algebraic Techniques, SMB-060
Expand and simplify the expression `(a+b)^2-(a-b)^2` (2 marks)
Algebraic Techniques, SMB-059
Expand and simplify the expression `(4-7x)^2` (2 marks)
Algebraic Techniques, SMB-058
Expand and simplify the expression `(c-2)^2` (2 marks)
Algebraic Techniques, SMB-057
Expand and simplify the expression `(2x-5)^2` (2 marks)
Algebraic Techniques, SMB-056
Expand and simplify the expression `(2y-3)(2y+3)` (2 marks)
Algebraic Techniques, SMB-055
Expand and simplify the expression `(p-4q)(p+4q)` (2 marks)
Algebraic Techniques, SMB-054
Expand and simplify the expression `(3a+1)(2-a)+2a+4` (2 marks)
Algebraic Techniques, SMB-053
Simplify the expression `(4y+1)/8-(6-2y)/3` (2 marks)
Algebraic Techniques, SMB-052
Simplify the expression `(3a+2)/3-(2a-1)/5` (2 marks)
Algebraic Techniques, SMB-051
Simplify the expression `x/4-(x+2)/5` (2 marks)
Algebraic Techniques, SMB-050
Simplify the expression `(2p-1)/2+(p+1)/5` (2 marks)
Algebraic Techniques, SMB-049
Simplify the expression `(x-4)/3+(2x+1)/6` (2 marks)
Algebraic Techniques, SMB-048
Factorise the expression `b^2+4b-12` (2 marks)
Algebraic Techniques, SMB-047
Factorise the expression `-a^2+3a+10` (2 marks)
Algebraic Techniques, SMB-046
Factorise the expression `n^2+5n-24` (2 marks)
Algebraic Techniques, SMB-045
Fully factorise the expression `6x^2-8x-8` (2 marks)
Algebraic Techniques, SMB-044
Factorise the expression `2p^2-5p-12` (2 marks)
Algebraic Techniques, SMB-043
Factorise the expression `y^2-2y-15` (2 marks)
Algebraic Techniques, SMB-042
Factorise the expression `x^2+6x+8` (2 marks)
Algebraic Techniques, SMB-041
Expand and simplify the expression `(4x-3y)(y-x)` (2 marks)
Algebraic Techniques, SMB-040
Expand and simplify the expression `(7m-3)(m-2)` (2 marks)
Algebraic Techniques, SMB-039
Expand and simplify the expression `(a-b)(3a-2b)` (2 marks)
Algebraic Techniques, SMB-038
Expand and simplify the expression `(2p-3)(p+1)` (2 marks)
Algebraic Techniques, SMB-037
Expand and simplify the expression `(2x-1)(2x+1)` (2 marks)
Algebraic Techniques, SMB-036
Simplify the expression `3/(4x)+2/(5x)` (2 marks)
Algebraic Techniques, SMB-035
Simplify the expression `5/(4a)-1/(3a)` (2 marks)
Algebraic Techniques, SMB-034
Simplify the expression `3/x-1/(2x)` (2 marks)
Algebraic Techniques, SMB-033
Simplify the expression `(36p^2q^4)/7 xx 14/(4p^3q)` (2 marks)
Algebraic Techniques, SMB-032
Simplify the expression `(x^2y^5)/6 xx 18/(x^2y^2)` (2 marks)
Algebraic Techniques, SMB-031
Simplify the expression `(3a^2)/(12b^4) -: (9a^3)/(4b)` (2 marks)
Algebraic Techniques, SMB-030
Simplify the expression `(3xy)/4 xx 12/(4x)` (2 marks)
Algebraic Techniques, SMB-029
Simplify the expression `(24p^3q^2)/(8p^2q)` (2 marks)
Algebraic Techniques, SMB-028
Simplify the expression `(18a^2b)/(3ab^3)` (2 marks)
Algebraic Techniques, SMB-027
Simplify the expression `(12y^3)/(4y^2)` (2 marks)
Algebraic Techniques, SMB-026
Expand and simplify the expression
`13-3(x-4)` (2 marks)
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