# A rectangle has width 2^(1/3)m and length 4^(1/3)m. What is the area of the rectangle?

##### 2 Answers

#### Explanation:

The width of the rectangle is

We have:

So, the length of the rectangle can be written as

Area of a rectangle is given by the length multiplied by the width. So we have,

Recall that

But,

Another important fact is that

So, the area of this rectangle is

The area of the rectangle is

#### Explanation:

Before we start, let's revise the exponent rules,

- Product rule:
#a^x xxa^y=a^(x+y# - Quotient rule:
#a^x -:a^y=a^(x-y# - Power rule:
#(a^x)^y=a^(xy)# - Power of a product rule:
#(ab)^x=a^x xx b^x# - Power of a quotient rule:
#(a/b)^x=(a^x)/(b^x)# - Zero exponent:
#a^0=1# - Negative exponent:
#a^-x=1/a^x# - Fractional exponent:
#a^(x/y)=root(y)(a^x)#

Now let's begin, let the area of the rectangle be

Using rule 4 - Power of a product rule,

Therefore, the area of the rectangle is