Simplify `((4p^2)/8)^(-3)` and express as a fraction involving non-negative indices only. (3 marks)
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Simplify `((4p^2)/8)^(-3)` and express as a fraction involving non-negative indices only. (3 marks)
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`8/(p^6)`
`((4p^2)/8)^(-3)` | `=(4^(-3)xxp^((2xx-3)))/(8^(-3))` |
`= (8^(3)xxp^(-6))/(4^(3))` | |
`= 8/(p^6)` |
Simplify `((3y^3)/2)^(-2)` and express as a fraction involving non-negative indices only. (3 marks)
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`4/(9y^6)`
`((3y^3)/2)^(-2)` | `=(3^(-2)xxy^((3xx-2)))/(2^(-2))` |
`= (2^(2)xxy^(-6))/(3^(2))` | |
`= 4/(9y^6)` |
Express `4a^(-5) -: 12a^4` as a fraction involving non-negative indices only. (1 mark)
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`1/(3a^9)`
`4a^(-5) -: 12a^4` | `=(4a^(-5))/(12a^4)` |
`= a^((-5-4))/3` | |
`= (a^(-9))/3` | |
`=1/(3a^9)` |
Express `(24p^(-3)q^4)/(8pq^(2))` as a fraction involving non-negative indices only. (1 mark)
`(3q^2)/p^4`
`(24p^(-3)q^4)/(8pq^(2))` | `=3p^((-3-1))q^((4-2))` |
`= 3p^(-4)q^2` | |
`= (3q^2)/p^4` |
Simplify the expression `(36t^4)/(9t^(-2))`. (1 mark)
`4t^6`
`(36t^4)/(9t^(-2))` | `= 4t^(4-(-2))` |
`= 4t^6` |
Simplify the expression `(16x^5)/(2x^(-3))`. (1 mark)
`8x^8`
`(16x^5)/(2x^(-3))` | `= 8x^(5-(-3))` |
`= 8x^8` |
Express `4^(-3)` as a fraction. (1 mark)
`1/64`
`4^(-3)` | `= 1/4^3` |
`= 1/64` |
Select the expression that is equivalent to `(4^(-3) ÷ 4^6)^3`
`A`
`(4^(-3) -: 4^6)^3` | `= (4^(-3-6))^3` |
`= (4^(-9))^3` | |
`= 4^(-9 xx 3)` | |
`= 4^(-27)` |
`=>A`
Which of the following has the same value as `7^(-11)?`
`D`
`7^(-11)=1/(7^11)`
`=>D`