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 squaredb. 3 to the 8 over 3 power inches squaredc. 9 inches squared d.9 to the 2 over 3 power inches squared2.)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 factorsb. By finding the quotient of the bases to be one fourth and simplifying the expressionc. By simplifying 8 to 23 to make both powers base two and subtracting the exponentsd. By simplifying 8 to 23 to make both powers base two and adding the exponents3.)the cube root of 2 to the seventh powera. 2 to the 3 over 7 powerb. 2 to the 7 over 3 powerc. 2^21d. 2^4,
Accepted Solution
A:
Answer 1) c. 9 inches squared 2) c. By simplifying 8 to 23 to make both powers base two and subtracting the exponents 3) b. 2 to the 7 over 3 power
Explanation. Question 1 The area of a rectangle is given by area=lΓw =γ81γ^(1/3)Γ3^(2/3) 3^(4/3)Γ3^(2/3)=3^(4/3+2/3) =3^(6/3)=3^2=9 inches squared
Question 2 Finding the 2^5/8=2^2 The steps for finding this is first to write 8 as 23. Then divide. 2^5/8=2^5/2^3 When dividing exponents with the same base you subtract the powers. =2^(5-3)=2^2
Question 3 The question wants us to solve, β(3^7 ).the cube root of a number can be written as a power of a third. So, β(3^7 )=3^(7Γ1/3 ) =3^(7/3)