What is the value of 4 to the power of 6 over 4 to the power of 8?

Group of answer choices

1 over 1024

1 over 256

1 over 64

1 over 16

1 answer

To find the value of \( \frac{4^6}{4^8} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this to the expression:

\[ \frac{4^6}{4^8} = 4^{6-8} = 4^{-2} \]

Now, \( 4^{-2} \) can be rewritten as \( \frac{1}{4^2} \).

Calculating \( 4^2 \):

\[ 4^2 = 16 \]

Thus,

\[ 4^{-2} = \frac{1}{16} \]

So the value of \( \frac{4^6}{4^8} \) is \( \frac{1}{16} \).

The correct answer is:

1 over 16.