Question

Raise the quantity in parentheses to the indicated exponent, and simply the resulting expression with positive exponents. (-4x⁻² y^(4)⁻² lease show all of the steps for your solution.

Answer 1

The expression (-4x⁻²y⁴)⁻² simplifies to 1/(16y⁸)x⁴. This involves applying the exponent to each factor inside the parentheses, which affects the coefficient and each variable's exponent.

Step-by-step explanation:

When you are asked to raise the quantity in parentheses to the indicated exponent and simplify the expression, you must apply the exponent to every factor inside the parentheses. The expression to simplify is (-4x-2y⁴)⁻². To do this, you raise both the coefficient (-4) and the variables (x⁻² and y⁴) to the power of -2.

• Multiply the exponent of each variable by -2: x-2*-2 = x⁴ and y4*-2 = y⁻⁸.
• Raise -4 to the power of -2: (-4)⁻² = 1/16 because a negative exponent indicates taking the reciprocal of the base raised to the positive of that exponent.
• Combine the simplified terms: (1/16)x⁴y⁻⁸.
• Since we want only positive exponents, we need to take the reciprocal of y-⁸, which gives us y⁸ in the denominator.

The final simplified expression is 1/(16y⁸)x⁴.