Which of the following is a cube squareroot function Simplif

Which of the following is a cube squareroot function? Simplify a^-3/2 middot 4a^5/3 b^1/2 6/b^1/4 12a^5/b^4 4a^1/6 b^1/2 6a^3/4 Which is an element of the range of the graphed function? -1 -3 2 5 Solve the following exponential equation: 243^-2x middot 27^x + 2 = 27 x = -1/5 x = 3/7 x = -3/5 x = 3/13

Solution

7) Graph of cube root function : y = (x)^1/3

when it is shifted downwards y = (x)^1/3 -4

It resembles Option B

8) a^(-3/2)*4(a)^(5/3)*b^1/2

= a^(-3/2+5/3)*4*b^1/2

= a^(1/6)*4*b^1/2

= 4a^(1/6)(b)^1/2

Option H

9) Graph lies across the horizontal line y =3 and extends above it

So, range : (3, inf)

So, y =5 is in range

Option D

10. 243^(-2x)*27^(x+2) = 27

factorise 243 = 3*81 = 3*3^2*3^2 = 3^5

27 = 3^3

So, 243^(-2x)*27^(x+2) = 3^(-10x)*3^(3x+6) = 27

3^(-10x +3x +6) = 3^3

Equate the exponents on both sides as base is same:

-10x +3x +6 =3

-7x = -3

x= 3/7

Option G

Option