smc-4228-50-Negative indices

Indices, SMB-022

Simplify `((4p^2)/8)^(-3)` and express as a fraction involving non-negative indices only. (3 marks)

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

Show Answers Only

`8/(p^6)`

Show Worked Solution

`((4p^2)/8)^(-3)`	`= ((p^2)/2)^(-3)`
	`=p^(2xx -3)/(2^(-3))`
	`= (p^(-6))/(2^(-3))= (2^(3))/(p^(6))`
	`= 8/(p^6)`

Indices, SMB-021

Simplify `((3y^3)/2)^(-2)` and express as a fraction involving non-negative indices only. (3 marks)

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

Show Answers Only

`4/(9y^6)`

Show Worked Solution

`((3y^3)/2)^(-2)`	`=(3^(-2)xxy^((3xx-2)))/(2^(-2))`
	`= (2^(2)xxy^(-6))/(3^(2))`
	`= 4/(9y^6)`

Indices, SMB-020

Express `4a^(-5) -: 12a^4` as a fraction involving non-negative indices only. (1 mark)

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

Show Answers Only

`1/(3a^9)`

Show Worked Solution

`4a^(-5) -: 12a^4`	`=(4a^(-5))/(12a^4)`
	`= a^((-5-4))/3`
	`= (a^(-9))/3`
	`=1/(3a^9)`

Indices, SMB-019

Express `(24p^(-3)q^4)/(8pq^(2))` as a fraction involving non-negative indices only. (1 mark)

Show Answers Only

`(3q^2)/p^4`

Show Worked Solution

`(24p^(-3)q^4)/(8pq^(2))`	`=3p^((-3-1))q^((4-2))`
	`= 3p^(-4)q^2`
	`= (3q^2)/p^4`

Indices, SMB-018

Simplify the expression `(36t^4)/(9t^(-2))`. (1 mark)

Show Answers Only

`4t^6`

Show Worked Solution

`(36t^4)/(9t^(-2))`	`= 4t^(4-(-2))`
	`= 4t^6`

Indices, SMB-017

Simplify the expression `(16x^5)/(2x^(-3))`. (1 mark)

Show Answers Only

`8x^8`

Show Worked Solution

`(16x^5)/(2x^(-3))`	`= 8x^(5-(-3))`
	`= 8x^8`

Indices, SMB-014

Express `4^(-3)` as a fraction. (1 mark)

Show Answers Only

`1/64`

Show Worked Solution

`4^(-3)`	`= 1/4^3`
	`= 1/64`

Indices, SMB-006 MC

Select the expression that is equivalent to `(4^(-3) ÷ 4^6)^3`

`4^(-27)`
`4^(-9)`
`4^(-54)`
`4^(-6)`

Show Answers Only

`A`

Show Worked Solution

`(4^(-3) -: 4^6)^3`	`= (4^(-3-6))^3`
	`= (4^(-9))^3`
	`= 4^(-9 xx 3)`
	`= 4^(-27)`

`=>A`

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`

Show Answers Only

`D`

Show Worked Solution

`7^(-11)=1/(7^11)`

`=>D`