Find the numerical equivalent of 4 ^ 9 * 4 ^ - 7 (1 point)
4
4 ^ 16
4 ^ 2
16
The numerical equivalent of 4 ^ 9 * 4 ^ -7 is 4 ^ 2, which is equal to 16.
To find the numerical equivalent of 4^9 * 4^-7, we can use the properties of exponents.
First, let's simplify the exponents separately.
4^9 can be written as (4^2)^4, applying the power of a power rule:
4^9 = (4^2)^4 = 16^4
Similarly, 4^-7 can be written as 1/(4^7), applying the negative exponent rule:
4^-7 = 1/(4^7) = 1/16384
Now, let's multiply these two simplified expressions:
(16^4) * (1/16384)
To simplify further, we can rewrite 16^4 as (2^4)^4, applying the power of a power rule:
16^4 = (2^4)^4 = 2^16
Substituting this value into the expression, we get:
(2^16) * (1/16384)
To multiply these two terms, we add the exponents since the base is the same:
2^(16 - 14) = 2^2 = 4
Therefore, the numerical equivalent of 4^9 * 4^-7 is 4.