The answer is: " - 1,458 ".
Explanation:
We are asked to simplify: " -2(3²)³ " ; into standard form.
Take note of the 'order of operations'—by using the mnemonic:
"Please Excuse My Dear Aunt Sally."
in which:
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Parentheses, if they occur, take top priority.
then :
Exponents, if they occur, take second priority.
then :
Multiplication—and/or:
Division—if they occur; take third priority; yet, multiplication does not necessarily take priority over division. Rather, multiplication and/or division, if Either occurs, take the next priority—in the order in which they occur from the far left of the expression to the end.
then :
Addition—and/or:
Subtraction—if they occur; take the last priority; yet, addition does not necessarily take priority over subtraction. Rather, addition and/or subtraction, if Either occurs, take the last priority—in the order in which they occur from the far left of the expression to the end.
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Our given expression: " -2(3²)³ " ; is the same as:
" - 2* (3²)³ " ; We have parentheses, exponents, and multiplication;
So; we need to find the value of: " (3²)³ " ;
and multiply that value by -2 ;
So, let's start with calculating: " (3²)³ " ;
Method 1)
" (3²)³ = (3* 3)³ = 9³ = 9 * 9 * 9 = (9 * 9) * 9 = 81 * 9 = 729 " .
Method 2)
Note the multiplication property of exponents:
(aᵇ)ᶜ = a⁽ ᵇ *ᶜ ⁾ ;
As such: " (3²)³ = 3⁽²*³⁾ = 3⁶ " ;
= 3 * 3 * 3 * 3 * 3 * 3 ;
= (3 * 3) * 3 * 3 * 3 * 3 ;
= 9 * 3 * 3 * 3 * 3 ;
= (9 * 3) * 3 * 3 * 3 ;
= (27) * 3 * 3 * 3 ;
= (27) * (9)* 3 ;\
= 27 * 27 ;
₁
₄
2 7
* 2 7
¹ 1 8 9
⁺_5 4
7 2 9
= 729
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Now, multiply 729 by -2 ;
{Note that a negative value, when multiplied by a positive value, results in a negative value.}\
₁
7 2 9
* - 2
- 1 4 5 8 ; which is our answer to: " -2(3²)³ " ; written in standard form.
The answer is: " - 1,458 ".
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Hope this is helpful to you.
Best of luck to you!
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