2^98×3^46=2^100×3^200
Such that they become perfect cube. How to solve this?
Answers
Need to multiply by 2 * 3² with 2⁹⁸ * 3⁴⁶
Step-by-step explanation:
Taking both term separate
2⁹⁸ * 3⁴⁶ and 2¹⁰⁰ * 3 ²⁰⁰
2 & 3 are co-prime
2⁹⁸ * 3⁴⁶
= 2⁹⁶ * 2² * 3⁴⁵ * 3
= (2³²)³ * 2² * (3¹⁵)³ * 3
To make it perfect cube
we need to multiply by 2 * 3²
= (2³²)³ * 2² * (3¹⁵)³ * 3 * 2 * 3²
= (2³²)³ * 2³ * (3¹⁵)³ * 3³
= (2³³)³ * (3¹⁶)³
= ( 2³³ * 3¹⁶)³
2¹⁰⁰ * 3 ²⁰⁰
= 2⁹⁹ * 2 * 3¹⁹⁸ * 3²
= (2³³)³ * 2 * (3⁶⁶)³ * 3²
To make it perfect cube
we need to multiply by 2² * 3
= (2³³)³ * 2 * (3⁶⁶)³ * 3² * 2² * 3
= (2³³)³ * 2³ * (3⁶⁶)³ * 3³
= (2³⁴)³ * (3⁶⁷)³
= (2³⁴ * 3⁶⁷)³
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