Question

Simplity. White the arower using positive exponent (2⁻²x⁷y⁻⁸)/(x⁻⁵y⁻¹⁵)

Answer 1

To simplify (2⁻²x⁷y⁻⁸)/(x⁻⁵y⁻¹⁵) and write it with positive exponents, we start by recognizing 2⁻² as 1/4 and then subtract the exponents of like bases: x⁷ divided by x⁻⁵ gives x¹² and y⁻⁸ divided by y⁻¹⁵ gives y⁷, resulting in the simplified expression 1/4 ⋅ x¹² ⋅ y⁷ with positive exponents.

Step-by-step explanation:

To simplifying the expression (2⁻²x⁷y⁻⁸)/(x⁻⁵y⁻¹⁵) and writing the answer using positive exponents. To do this, we will use the laws of exponents, which allow us to subtract the exponents when dividing like bases.

First, we address the 2 with a negative exponent:

• 2⁻² can be written as ⅖² or 1/4.

Next, we simplify the x and y terms by subtracting the exponents in the numerator from the exponents in the denominator:

For x: x⁷ / x⁻⁵ = x¹² (because 7 - (-5) = 7 + 5 = 12)
For y: y⁻⁸ / y⁻¹⁵ = y⁷ (because -8 - (-15) = -8 + 15 = 7)

Putting it all together:

(2⁻²x⁷y⁻⁸)/(x⁻⁵y⁻¹⁵) = 1/4 ⋅ x¹² ⋅ y⁷

This simplification now uses positive exponents for the variables x and y.