Simplify the expression (6x^3 divided by 3x^4)^2
2 answers:
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Answer:
key the numbers into your calculator and execute the multiplication function
Step-by-step explanation:
Details vary with calculator model. Read your manual.
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There are many ways to work a problem of this nature by hand or in your head. The second attachment shows a couple of them.
<em>Long multiplication</em>
Essentially, every digit in one number needs to be multiplied by every digit in the other number, and the results combined according to their place value. The diagram on the left is a method that has you put the product of the top digit and the right digit into the box with "tens" and "ones" separated by a diagonal line.
After you've filled in the products of all the digits, you add them along diagonal "columns", putting the sum at the bottom or to the left. Any "carry" from the sum will add to the next "column" to the left or above. For example, the product digit 3 is arrived at by adding the 8, 2, and 3 along the diagonal. That sum results in a "carry" of 1 that gets added to the 4, 6, and 0 in the diagonal "column" above it.
As with any multiplication of decimals, the number of decimal digits in the product is the same as the total of the numbers of decimal digits in the multiplicands. (2+1=3)
<em>Mental math</em>
Both these numbers are multiplies of 9, so the product can be found different ways using that fact. The number 1.8 is 2 - 0.2, so the product can be found as ...
0.63 × 1.8 = 0.63 × (2 -0.2) = (0.63×2) - (0.63×0.2)
= 1.26 -0.126 = 1.134
Multiplication by 2 is easily done in your head. The subtraction of one 3-digit number from another may be a little harder to do, but is probably less work than the long multiplicatin described above.
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<em>Alternative mental math</em>
The product of one number and the other, as described above, is the product of each digit in one number with each digit in the other number, paying attention to place value.
With decimal points removed, the numbers are 63 and 18, and their product is ...
6·1 × 100 + (6·8 +3·1) × 10 + 3·8
= 600 +510 +24
= 1110 +24
= 1134
The the desired product is this value with the decimal point put 3 places from the right: 1.134
