Math  /  Numbers & Operations

QuestionDirections: Find the cube of each number. Show your work! 93=9,9,9×9=81×915.1515153=13375123=33=72913= 14.14:14 143=83=53=13.13R133=219763=6.610(21623=43=113=103=73=163=\begin{array}{l} 9^{3}=9,9,9 \times 9 \\ =81 \times 9 \\ \begin{array}{l} 15.15 \cdot 15 \\ 15^{3}=\frac{1}{3} 375 \end{array} \\ 12^{3}= \\ 3^{3}= \\ 729 \\ 1^{3}= \\ \text { 14.14:14 } \\ 14^{3}= \\ 8^{3}= \\ 5^{3}= \\ 13.13 \cdot R \\ 13^{3}=2197 \\ 6^{3}=\frac{6.6 \cdot 10}{(216} \\ 2^{3}= \\ 4^{3}= \\ 11^{3}= \\ 10^{3}= \\ 7^{3}= \\ 16^{3}= \end{array}

Studdy Solution

STEP 1

What is this asking? We need to calculate the cube of a bunch of numbers, which means multiplying each number by itself three times! Watch out! Don't multiply by 3; multiply the number by itself *three* times.
Also, large numbers multiplied together can get big fast, so double-check those calculations!

STEP 2

1. Calculate the cubes.

STEP 3

Let's **start** with 939^3.
This means 9999 \cdot 9 \cdot 9.
First, 99=819 \cdot 9 = \textbf{81}.
Then, 819=72981 \cdot 9 = \textbf{729}.
So, 93=7299^3 = \textbf{729}.

STEP 4

Next up, 12312^3.
This is 12121212 \cdot 12 \cdot 12.
We have 1212=14412 \cdot 12 = \textbf{144}.
Then, 14412=1728144 \cdot 12 = \textbf{1728}.
Therefore, 123=172812^3 = \textbf{1728}.

STEP 5

Now for 333^3, which is 3333 \cdot 3 \cdot 3.
First, 33=93 \cdot 3 = \textbf{9}.
Then, 93=279 \cdot 3 = \textbf{27}.
So, 33=273^3 = \textbf{27}.

STEP 6

131^3 is easy!
It's just 111=11 \cdot 1 \cdot 1 = \textbf{1}.

STEP 7

Time for 14314^3: 14141414 \cdot 14 \cdot 14.
First, 1414=19614 \cdot 14 = \textbf{196}.
Then, 19614=2744196 \cdot 14 = \textbf{2744}.
So, 143=274414^3 = \textbf{2744}.

STEP 8

Let's do 838^3.
That's 8888 \cdot 8 \cdot 8.
We have 88=648 \cdot 8 = \textbf{64}, and then 648=51264 \cdot 8 = \textbf{512}.
Therefore, 83=5128^3 = \textbf{512}.

STEP 9

535^3 is 5555 \cdot 5 \cdot 5.
First, 55=255 \cdot 5 = \textbf{25}, and then 255=12525 \cdot 5 = \textbf{125}.
So, 53=1255^3 = \textbf{125}.

STEP 10

13313^3 is 13131313 \cdot 13 \cdot 13.
First, 1313=16913 \cdot 13 = \textbf{169}.
Then, 16913=2197169 \cdot 13 = \textbf{2197}.
Thus, 133=219713^3 = \textbf{2197}.

STEP 11

For 636^3, we have 6666 \cdot 6 \cdot 6. 66=366 \cdot 6 = \textbf{36}, and 366=21636 \cdot 6 = \textbf{216}.
So, 63=2166^3 = \textbf{216}.

STEP 12

232^3 is a quick one: 222=82 \cdot 2 \cdot 2 = \textbf{8}.

STEP 13

434^3 is 4444 \cdot 4 \cdot 4. 44=164 \cdot 4 = \textbf{16}, and 164=6416 \cdot 4 = \textbf{64}.
So, 43=644^3 = \textbf{64}.

STEP 14

Let's tackle 11311^3: 11111111 \cdot 11 \cdot 11. 1111=12111 \cdot 11 = \textbf{121}, and then 12111=1331121 \cdot 11 = \textbf{1331}.
Therefore, 113=133111^3 = \textbf{1331}.

STEP 15

10310^3 is 101010=100010 \cdot 10 \cdot 10 = \textbf{1000}.

STEP 16

Now for 737^3, which is 7777 \cdot 7 \cdot 7. 77=497 \cdot 7 = \textbf{49}, and 497=34349 \cdot 7 = \textbf{343}.
So, 73=3437^3 = \textbf{343}.

STEP 17

Finally, 16316^3: 16161616 \cdot 16 \cdot 16.
First, 1616=25616 \cdot 16 = \textbf{256}.
Then, 25616=4096256 \cdot 16 = \textbf{4096}.
So, 163=409616^3 = \textbf{4096}.
And we're done!

STEP 18

93=7299^3 = 729 153=337515^3 = 3375 123=172812^3 = 172833=273^3 = 2713=11^3 = 1143=274414^3 = 274483=5128^3 = 51253=1255^3 = 125133=219713^3 = 219763=2166^3 = 21623=82^3 = 843=644^3 = 64113=133111^3 = 1331103=100010^3 = 100073=3437^3 = 343163=409616^3 = 4096

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