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

#### Dnichol016

##### New member
2[1/4 + 4(36 divided by 12)]

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

#### MarkFL

Staff member
Hello, and welcome to MHB! As written, the expression evaluates to:

$$\displaystyle \frac{49}{2}$$

Are you certain you have copied it correctly?

• topsquark

#### HallsofIvy

##### Well-known member
MHB Math Helper
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!

• topsquark

#### Dnichol016

##### New member
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

#### MarkFL

Staff member
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:

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

• anemone and Joppy

Thank yo so much