Question

Can someone help me with this as well? Thank you so much!

Answer 1

here are the exponential rules:

`(ab)^c=(a^c)(b^c)`

`(1)/(a^b)=a^(-b)`

`(a^b)^c=a^(bc)`

`(a^b)(a^c)=a^(b+c)`

if
`a^b=c^b` and b=b, then a=c

a.

she made a mistake in the 1st step because she used a positive exponent instead of a negative one for a fraction

in mathspeak: 1/16=1/(2^4)=2^-4, not 2^4

b.

`2^(2x-3)=((1)/(16))^(3x+9)`

`2^(2x-3)=((1)/(2^4))^(3x+9)`

`2^(2x-3)=(2^(-4))^(3x+9)`

`2^(2x-3)=2^(-4(3x+9))`

`2^(2x-3)=2^(-12x-36)`

`2x-3=-12x-36`

`-3=-14x-36`

`33=-14x`

`x=(-33)/(14)`

Answer 2

Leah made a mistake in the first step, writing
`\frac 1 {16}` as
`2^4` when it's really
`2^(-4)`.

`2^(2x-3) = (2^(-4))^(3x + 9) = 2^(-12x - 36)`

`2x - 3 = -12x - 36`

`14x =-33`

`x = -(33)/(14)`

Check:

2x-3 = -33/7 - 21/7 = -54/7

-4(3x+9) = -4(-99/14 + 126/14) = -4(27/14) = -54/7 check

Answer: x=-33/14