The expression (5/m)⁻² which is a fraction with a negative index is simplified to be m²/25 using the law of indeces.
One of the laws of indeces states for any expression in the form (a/b)⁻ˣ can be simplified to be (bˣ/aˣ). Thus for the expression (5/m)⁻², we simplify as follows:
(5/m)⁻² = 1 ÷ (5/m)²
(5/m)⁻² = 1 ÷ (5³/m²)
(5/m)⁻² = 1 ÷ (25/m²)
(5/m)⁻² = 1 × (m²/25) {changing division to multiplication}
(5/m)⁻² = m²/25
Therefore, by indeces law, the expression (5/m)⁻² is simplified to be m²/25.
Complete question:
Simplify the expression the expression (5/m)⁻².