Arectangle has a length of \sqrt[3]{81} and a width of 3^{\frac{2}{3}} inches. find the area of the rectangle.

The area of the rectangle is 9.

Step-by-step explanation:

The first thing to take into account is that the area of a rectangle is obtained by multiplying its length and width.

The problem says that the length is and the width is . So, to find the area we must replace the values of length and width into the previous expression.

The previous seems to be difficult but with a little of manipulation we can get a result without a calculator.

First step: the term could be written as exponential expression.

Second step: the term could be written in other way.

Third step: in the same way, the term could be written in other way taking into account that .

Forth step: the two terms must have the same base to apply other exponential rules; for example, the base could be 9.

Fifth step: as both terms have the same base, we must add the exponents and simplify the expression.

Thus, the area of the rectangle is 9.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

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step-by-step explanation: ; )