Which expression is equivalent to RootIndex 3 StartRoot 64 a Superscript 6 Baseline b Superscript 7 Baseline c Superscript 9 Baseline EndRoot?
2 a b c squared (RootIndex 3 StartRoot 4 a squared b cubed c EndRoot)
4 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)
8 a cubed b cubed c Superscript 4 Baseline (RootIndex 3 StartRoot b c EndRoot)
8 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)

Which expression is equal to ?

The correct answer is B.

Step-by-step explanation:

Inside of the radical you have . If you find the cube root of that, you get 4a^2. Go ahead and write that outside of the parenthesis:

If you re-write what is inside of the radical, you get:

Basically I expanded what was inside of the radical so I could find the cube roots of b^7 and c^9.

Now, take the cube root of b^7:

Notice how I could only factor out the two "b^3" that were inside the radical symbol, and how I left the b^1 inside the radical symbol because I couldn't factor it out.

Let's now get the cube root of c^9. Since it's a perfect cube, there won't be any "c"s left inside of the radical symbol:

oof

step-by-step explanation:

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: