Select the equivalent expression. \left(\dfrac{x^{4}}{7^{-8}}\right)^ {-7}=?(
7
−8

x
4

​
)
−7
=?left parenthesis, start fraction, x, start superscript, 4, end superscript, divided by, 7, start superscript, minus, 8, end superscript, end fraction, right parenthesis, start superscript, minus, 7, end superscript, equals, question mark
Choose 1
Choose 1

(Choice A)
A
\dfrac{x^{28}}{7^{56}}
7
56

x
28

​
start fraction, x, start superscript, 28, end superscript, divided by, 7, start superscript, 56, end superscript, end fraction

(Choice B)
B
{x^{-28}}\cdot{7^{-56}}x
−28
⋅7
−56
x, start superscript, minus, 28, end superscript, dot, 7, start superscript, minus, 56, end superscript

(Choice C)
C
\dfrac{x^{28}}{7^{-56}}
7
−56

x
28

​

b

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:

b. b < 1 might be the correct answer

mr. india