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Parentheses and brackets: Evaluate 2³[1/4+4(36÷12)]

Dnichol016

New member
May 11, 2020
4
2[1/4 + 4(36 divided by 12)]

its 2 to the 3rd power. How do you solve this?
 

MarkFL

Pessimist Singularitarian
Staff member
Feb 24, 2012
13,684
St. Augustine, FL.
Hello, and welcome to MHB! :)

As written, the expression evaluates to:

\(\displaystyle \frac{49}{2}\)

Are you certain you have copied it correctly?
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
2[1/4 + 4(36 divided by 12)]

its 2 to the 3rd power. How do you solve this?
The "deepest" parentheses are "(36 divided by 12)" which is 3 so
that reduces to "2[1/4+ 4(3)]= 2[1/4+ 12]. Now 1/4+ 12= 1/4+ 48/4= 49/4
so we can reduce further to 2[49/4]= 49/2. That is NOT 2^3= 8.

It is possible that you intended the "4+ 4(36 divided by 23)" to all be in the denominator, not just the 4. That would require one more set of brackets:
2[1/{4+ 4(36 divided by 23)}]= 2[1/{4+ 4(3)}]= 2[1/(4+ 12)]= 2[1/16]= 2/16= 1/8.

But 1/8 is still not 8!
 

Dnichol016

New member
May 11, 2020
4
Hello, and welcome to MHB! :)

As written, the expression evaluates to:

\(\displaystyle \frac{49}{2}\)

Are you certain you have copied it correctly?
Yes it’s in my grandsons homework
 

Dnichol016

New member
May 11, 2020
4
2833EABD-6C42-4473-808B-9E229704D990.jpeg
 

MarkFL

Pessimist Singularitarian
Staff member
Feb 24, 2012
13,684
St. Augustine, FL.
Okay, we are given to evaluate:

\(\displaystyle 2^3\left[\frac{1}{4}+4(36\div12)\right]\)

Do the division within the innermost brackets:

\(\displaystyle 2^3\left[\frac{1}{4}+4(3)\right]\)

Do the indicated multiplication within the brackets:

\(\displaystyle 2^3\left[\frac{1}{4}+12\right]\)

Do the indicated addition within the brackets:

\(\displaystyle 2^3\left[\frac{49}{4}\right]\)

Rewrite \(2^3\) as \(8\):

\(\displaystyle 8\left[\frac{49}{4}\right]\)

Do the indicated multiplication:

\(\displaystyle 8\left[\frac{49}{4}\right]=2\cdot49=98\)
 

Dnichol016

New member
May 11, 2020
4
Thank yo so much