Simplify:
4s raised to the negative 2 power - (4t)raised to the -2 power
4s^2 - (4t)^-2
what about it?
Are we factoring?
If so, I see the difference of squares
= 4(s+t^-1)(s-t^-1)
or
= 4(s+1/t)(s-1/t)
No the question only says to simplify and the problem was 4s^-2-(4t)^-2
sorry, did not see that first -2
ok, factoring is simplifying
or you could so this
4/s^2 - 1/(16t^2)
= (64t^2 - s^2)/(16s^2t^2)
= (8t+s)(8t-s)/(16s^2t^2)
my revised solution for the above:
4s^-2 - 16t^-2
= 4(s^-1 + 2t^-1)(s^-1 - 2t^-1)
or
= 4(1/s + 2/t)(1/s - 2/t)
To simplify the expression 4s^(-2) - (4t)^(-2), we need to apply the laws of exponents.
The first step is to rewrite the negative exponents as positive exponents by moving the terms to the denominator:
4s^(-2) can be rewritten as 4 / s^2, and
(4t)^(-2) can be rewritten as 1 / (4t)^2.
Now, let's simplify further:
4 / s^2 - 1 / (4t)^2
Next, we need to simplify both fractions by finding a common denominator. The least common multiple (LCM) of the denominators s^2 and (4t)^2 is (s^2 * (4t)^2).
Multiplying the first fraction by (4t)^2 / (4t)^2 and the second fraction by s^2 / s^2, we have:
(4 * (4t)^2) / (s^2 * (4t)^2) - (s^2) / (s^2 * (4t)^2)
Simplifying the numerator gives us:
(4 * 16t^2) / (s^2 * 16t^2) - (s^2) / (s^2 * (4t)^2)
Which simplifies to:
64t^2 / (s^2 * 16t^2) - (s^2) / (s^2 * 16t^2)
Now, we can combine the fractions:
(64t^2 - s^2) / (s^2 * 16t^2)
Therefore, the simplified expression is (64t^2 - s^2) / (s^2 * 16t^2).