if 4 ^ x = 7, what does 4 ^ - 2x equal?

Question

do i need to find the intersection of 4^x and 7, then plug that # into 4 ^ - 2x ? thanks for your help.

Answer 1

Usually in sums like these you have to express the asked quantity in terms of the given quantity, in this case 4^ -2x has to be expressed in terms of 4^x.
So using properties of exponents,
4^ -2x = (4^ x ) ^ -2
since 4^ x = 7
4^ -2x = 7 ^ -2 = 1/49

Answer 2

4 ^ (-2x) = 1 / 4^(2x) = 1/4^x * 1/4^x = 1/7 * 1/7 = 1/49

Answer 3

4^-2x=(4^x)^-2=7^-2
=1/(7^2)=1/49

Answer 4

4^(-2x) = 1/(4^(2x)) = 1/((4^x)^2)

as you already know 4^x = 7, so

1/((4^x)^2) = 1/(7^2) = 1/49

Answer 5

4^{-2x}=(4^x)^{-2}
=7^{-2}=1/49

Answer 6

^?

4 to the power of what?

Answer 7

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Would you like an apple pie with that?
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