Answer:
Only options, A and E give 625/n¹² on simplification. The other options do not apply.
(5n⁻³)⁴ = (625/n¹²)
(25n⁻⁶)² = (625/n¹²)
Step-by-step explanation:
625/n¹²
a) (5n⁻³)⁴
According to the law of indices, this becomes
(5⁴)(n⁻³)⁴ = 625(n⁻¹²) = 625/n¹²
This applies!
b) (5n⁻³)⁻⁴
According to the law of indices, this becomes
(5⁻⁴)(n⁻³)⁻⁴ = (n¹²)/625 = n¹²/625
Does Not apply!
c) (5n⁻⁴)³
This becomes
(5³)(n⁻⁴)³ = 125n⁻¹² = 125/n¹²
Does Not apply!
d) (25n⁻⁶)⁻²
This becomes
(25⁻²)(n⁻⁶)⁻² = n⁻¹²/625 = 1/(625n¹²)
Does Not apply!
e) (25n⁻⁶)²
This becomes
(25²)(n⁻⁶)² = 625n⁻¹² = 625/n¹²
This applies!
