By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)
How to find an equivalent expression for a power function
In this question we have a power function with two variables and which has to be simplified by using power properties. The detailed procedure is shown below:
- y⁻⁸ · y³ · x⁰ · x⁻² Given
- (y⁻⁸ · y³) · (x⁰ · x⁻²) Associative property
- y⁻⁸⁺³ · x⁰⁻² Multiplication of powers of equal base
- y⁻⁵ · x⁻² Definition of addition and subtraction
- (y⁵)⁻¹ · (x²)⁻¹ Power of a power
- (y⁵ · x²)⁻¹ Power of a product
- 1 / (y⁵ · x²) Definition of division
- 1 / (x² · y⁵) Commutative property / Result
By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)
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