Final answer:
To simplify 4^2 * 4^-5, we can use the exponent rules. Evaluating this expression gives the value of 1/64.
Step-by-step explanation:
To find the equivalent value of 4^2 * 4^-5, we need to simplify the expression. We can use the exponent rules to do this. First, let's simplify the base of the exponents, which is 4. We can rewrite 4^-5 as 1/4^5. Now we can apply the exponent rule that states: a^m * a^n = a^(m + n). So, 4^2 * 4^-5 becomes 4^(2 + (-5)).
Adding the exponents gives us 4^(-3).
Remember that a negative exponent indicates the reciprocal of the base raised to the positive exponent.
So, 4^(-3) is equivalent to 1/4^3. Evaluating 4^3 gives us 64.
Therefore, 4^2 * 4^-5 is equal to 1/64.