4^2*(4^7)^-4

Answer 1

To simplify this expression, we first need to apply the exponent rule that states (a^m)^n = a^(m*n).

First, we simplify the expression within the parentheses:

4^7 = 16384

Now we rewrite the expression as:

4^2 * 16384^-4

Next, we simplify 16384^-4:

16384^-4 = 1 / 16384^4 = 1 / 1048576000000000

Now we rewrite the expression as:

4^2 * (1 / 1048576000000000)

Now we multiply 4^2 by the reciprocal of 1048576000000000:

4^2 * (1 / 1048576000000000) = 16 / 1048576000000000

Therefore, the simplified expression is:

16 / 1048576000000000