Question

A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.

3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared

Question 4(Multiple Choice Worth 2 points)

(MC)

Rewrite the rational exponent as a radical.

5 to the 3 over 4 power, to the 2 over 3 power

the cube root of 5 squared
the twelfth root of 5
the square root of 5
the cube root of 5 the fourth power

Question 5(Multiple Choice Worth 2 points)

(MC)

Rewrite the radical as a rational exponent.

the cube root of 2 to the seventh power

2 to the 3 over 7 power
2 to the 7 over 3 power
2 to the power of 21
2 to the power of 4

Answer 1

#1

`A= \sqrt[3]{81}*3^{ (2)/(3) }= \sqrt[3]{3^4}*3^{ (2)/(3) } = 3^{ (4)/(3) }*3^{ (2)/(3) }=3^{ (4)/(3) + (2)/(3) }=3^2=9`

9 inches squared


#2

`\left( 5^{ (3)/(4) } \right)^{ (2)/(3) }=5^{ (3)/(4) *(2)/(3) }=5^{ (1)/(2) }= √(5)`

C. the square root of 5


#3

`\sqrt[3]{2^7}=2^{ (7)/(3) }`

2 to the 7 over 3 power