Can someone please help me? Thanks!
simplify the following expression, and rewrite it in an equivalent form with positive exponents(4x^2)-^2
(4x^2)^-2 = 1 / (4x^2)^2 = 1 / 16x^4.
Of course, I can help you with that!
To simplify the expression (4x^2)^-2 and rewrite it with positive exponents, let's break it down step by step.
Step 1: Apply the exponent to the base inside the parentheses.
(4x^2)^-2 simplifies to 4^-2 * (x^2)^-2.
Step 2: Simplify the bases separately.
4^-2 = 1/4^2 = 1/16,
and (x^2)^-2 = x^(2*-2) = x^-4.
Step 3: Combine the simplified bases.
So, 4^-2 * (x^2)^-2 becomes 1/16 * x^-4.
Step 4: Convert the negative exponent to a positive exponent.
To do this, we use the property that x^-n is equivalent to 1/x^n. So, x^-4 becomes 1/x^4.
Step 5: Rewrite the final expression in the correct form.
Therefore, the expression (4x^2)^-2, simplified and rewritten with positive exponents, is 1/16 * 1/x^4, or simply 1/(16x^4).
I hope this helps! If you have any more questions or need further clarification, feel free to ask.