Simplify \(\frac{6^2\times 10^4\times 15^3}{2^6\times 3^5 \times 5^6}\)

Question

Question

This question was previously asked in

Kerala PSC Common Preliminary Exam (GRADUATE LEVEL) PYP - 047/23

Answer 1

Given:

Simplify \(\dfrac{6^2 × 10^4 × 15^3}{2^6 × 3^5 × 5^6}\)

Formula used:

Prime factorization and simplification of exponents

Calculation:

\(\dfrac{6^2 × 10^4 × 15^3}{2^6 × 3^5 × 5^6}\)

⇒ Rewrite the terms in their prime factorization:

6 = 2 × 3, 10 = 2 × 5, 15 = 3 × 5

⇒ \(\dfrac{(2 × 3)^2 × (2 × 5)^4 × (3 × 5)^3}{2^6 × 3^5 × 5^6}\)

⇒ Expand the powers:

\(\dfrac{2^2 × 3^2 × 2^4 × 5^4 × 3^3 × 5^3}{2^6 × 3^5 × 5^6}\)

⇒ Combine like terms:

\(\dfrac{2^{2+4} × 3^{2+3} × 5^{4+3}}{2^6 × 3^5 × 5^6}\)

⇒ \(\dfrac{2^6 × 3^5 × 5^7}{2^6 × 3^5 × 5^6}\)

⇒ Cancel out common terms:

2⁶, 3⁵, and 5⁶ cancel out:

⇒ Remaining term: \(\dfrac{5}{1} = 5\)

∴ The correct answer is option (4).

Download Solution PDF