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
$A= \sqrt[3]{81}*3^{ \frac{2}{3} }= \sqrt[3]{3^4}*3^{ \frac{2}{3} } = 3^{ \frac{4}{3} }*3^{ \frac{2}{3} }=3^{ \frac{4}{3} + \frac{2}{3} }=3^2=9$

9 inches squared


#2
$\left( 5^{ \frac{3}{4} } \right)^{ \frac{2}{3} }=5^{ \frac{3}{4} *\frac{2}{3} }=5^{ \frac{1}{2} }= \sqrt{5}$

C. the square root of 5


#3
$\sqrt[3]{2^7}=2^{ \frac{7}{3} }$

2 to the 7 over 3 power