Question

Solve (5⁻2 cdot x⁻1 / x⁴ y²).

a) (1/25x³ y²)
b) (1/10x⁵ y²)
c) (5x⁵/y²)
d) (10/x³ y²)

Answer 1

The simplified form of the expression (5^-2 ⋅ x^-1 / x^4 y^2) is (1/25x^3 y^2), which matches option (a) from the provided choices.

Step-by-step explanation:

To solve the expression (5⁻² ⋅ x⁻¹ / x⁴ y²), we need to simplify the terms using the properties of exponents. Rewriting 5⁻² as 1/5² and x⁻¹ as 1/x, we can simplify the expression as follows:

• Start with the original expression: (5⁻² ⋅ x⁻¹ / x⁴ y²).
• Convert negative exponents to fractions: ((1/5²) ⋅ (1/x) / x⁴ y²).
• Multiply fractions: ((1/25) ⋅ (1/x) / x⁴ y²).
• Multiply numerators and denominators: (1/25x⁵ y²).
• Simplify by combining the x terms: (1/25x³ y²).

So, the simplified form of the given expression is (1/25x³ y²), which corresponds to option (a).