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Number, NAP-K4-CA36

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

`4^(-27)` `4^(-9)` `4^(-54)` `(4^(-3 + 6))^4` `4^(-6)`
 
 
 
 
 
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`4^(-27)`

Show Worked Solution
`(4^(-3) ÷ 4^6)^3` `= (4^(-3 – 6))^3`
  `= (4^(-9))^3`
  `= 4^(-9 xx 3)`
  `= 4^(-27)`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 10, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-A4-NC27

Pamela has these four number cards.

Which two cards have the same value?

 
 
 
 
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Show Worked Solution
`9^2` `= 9xx9`
  `=81`
`3^4` `= 3 xx 3 xx 3 xx 3`
  `= 81`

 

`:. 9^2 and 3^4\ \ text(have the same value.)`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 9, smc-3143-40-Integer indices, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-B4-NC31

Which number has the largest value?

`1/3` `sqrt (0.16)` `0.38` `(0.6)^2`
 
 
 
 
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`sqrt (0.16)`

Show Worked Solution

`text(Express each as a decimal:)`

`1/3` `= 0.333…`
`sqrt(0.16)` `= 0.4`
`0.38` `= 0.38`
`(0.6)^2` `= 0.36`

 

`:. sqrt(0.16)\ text(is the largest value.)`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 10, smc-3173-30-Square roots, smc-3173-40-Integer Indices, smc-3173-70-Estimates (non calc), smc-890-30-Square roots, smc-890-40-Integer Indices, smc-890-70-Estimates (non calc)

Number, NAP-B4-NC16

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`
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`6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

Show Worked Solution
`6^3 xx 36^2` `= (6xx6xx6) xx (6xx6)^2`
  `= (6xx6xx6) xx (6xx6) xx (6 xx6)`
  `=6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 8, smc-3143-40-Integer indices, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-J4-NC08 SA

Complete the following equation,

`4^4 - 3^4 + 2^4 - 1^4 = `
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`190`

Show Worked Solution

`4^4 – 3^4 + 2^4 – 1^4`

`= (4 xx 4 xx 4 xx 4) – (3 xx 3 xx 3 xx 3) + (2 xx 2 xx 2 xx 2) – (1 xx 1 xx 1 xx1)`

`= 256 – 81 + 16 – 1`

`= 190`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 10, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-F4-NC08

1102 is a tri-square number because
 

`1^2 + 1^2 + 0^2 = 2`
 

The next tri-square number after 1102 is

`1104` `1113` `1209` `1126`
 
 
 
 
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`1113`

Show Worked Solution
`1^2 + 1^2 + 1^2` `= 1 + 1 + 1`
  `= 3`

 

`:. 1113\ text(is the next tri-square number.)`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 7, smc-3143-40-Integer indices, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-F4-NC11

`2^5 - 2^3 = ` 
 

Which number makes the expression above correct?

`4` `8` `24` `28`
 
 
 
 
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`24`

Show Worked Solution
`2^5 – 2^3` `=32 – 8`
  `=24`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 8, smc-3143-40-Integer indices, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-H4-NC07

`7 xx 2^3 =`

`28` `42` `56` `2744`
 
 
 
 
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`56`

Show Worked Solution
`7 xx 2^3` `= 7 xx 2 xx 2 xx 2`
  `= 56`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 7, smc-3143-40-Integer indices, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-H4-CA19

Which of the following has the same value as  `7^(-11)?`

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

Show Worked Solution

`1/7^11`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 9, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-H4-CA10

`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`
 
 
 
 
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`3^2 xx 2 xx 5 xx 2 xx 5`

Show Worked Solution

`30^2 = 900`

 

`3^2 xx 2 xx 5 xx 2 xx 5`

`= 3^2 xx 10 xx 10`

`= 900`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 7, smc-3143-40-Integer indices, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

Number, NAP-I4-CA02

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`
 
 
 
 
Show Answers Only

`2^3 xx 2^2`

Show Worked Solution
`2^3 xx 2^2` `= 8 xx 4`
  `= 32`

Filed Under: Basic Concepts and Calculations, Basic Concepts and Calculations, Basic Concepts and Calculations Tagged With: Band 6, smc-3143-40-Integer indices, smc-3173-40-Integer Indices, smc-890-40-Integer Indices

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