Question

Help please on properties of exponents? will give a medal!

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.

a. 3 to the 2 over 3 power inches squared

b. 3 to the 8 over 3 power inches squared

c. 9 inches squared

d.9 to the 2 over 3 power inches squared

2.)Explain how the Quotient of Powers was used to simplify this expression.

2 to the fifth power, over 8 = 2 to the 2nd power

a.By finding the quotient of the bases to be one fourth and cancelling common factors

b. By finding the quotient of the bases to be one fourth and simplifying the expression

c. By simplifying 8 to 23 to make both powers base two and subtracting the exponents

d. By simplifying 8 to 23 to make both powers base two and adding the exponents

3.)the cube root of 2 to the seventh power

a. 2 to the 3 over 7 power

b. 2 to the 7 over 3 power

c. 2^21

d. 2^4

Answer 1

For the first one use the fact that 81 = 3^4

Answer 2

is it b?

Answer 3

no

Answer 4

no its c!

Answer 5

because isnt the square root 0f 81 9?

Answer 6

\[\sqrt[3]{81}=\sqrt[3]{3^4}=(3^4)^{\frac{1}{3}}=3^{\frac{4}{3}}\]

Answer 7

oh so it's a?

Answer 8

\[3^{\frac{4}{3}}\times 3^{\frac{2}{3}}=3^{\frac{4}{3}+\frac{2}{3}}=3^{\frac{6}{3}}=3^2=9\]

Answer 9

wait, so then i was correct. the answer is C?

Answer 10

yes

Answer 11

thankyou! can you help me with the last two? :)

Answer 12

Replace 8 with 2^3 and then subtract the exponents.

Answer 13

For number 3 remember that in a fractional exponent, the top number is the power and the bottom number is the root.

Answer 14

is number 2 c?

Answer 15

yes

Answer 16

now i need help with 3 !

Answer 17

Mertsj
Medals 0

For number 3 remember that in a fractional exponent, the top number is the power and the bottom number is the root.

Answer 18

a?

Answer 19

What is the power given in the problem?

Answer 20

7

Answer 21

in a fractional exponent, the top number is the power and the bottom number is the root.

Answer 22

So you chose a which says the exponent is 3 over 7. In the fraction 3/7 is the top number 7?

Answer 23

oh! the power is 3

Answer 24

If the exponent is 3/7, then the power is 3. Does your problem say the power is 3?

Answer 25

no it doesn't the power is 2 in my problem, correct?

Answer 26

Oh wait, is the answer b?

Answer 27

yes

Answer 28

Thankyou :)

Answer 29

yw