Question

Simplify the expression:
$\frac{2^6 \times 5^4 \times 7^4}{10^4 \times 14^2}$

• A. 28
• B. 49
• C. 19
• D. 10

Answer 1

Answer:

B. 49

Simplify the expression:
$\frac{2^6 \times 5^4 \times 7^4}{10^4 \times 14^2}$

Rewrite denominators

$10^4 = (2 \times 5)^4 = 2^4 \times 5^4$
$14^2 = (2 \times 7)^2 = 2^2 \times 7^2$

Substitute

$\frac{2^6 \times 5^4 \times 7^4}{(2^4 \times 5^4)(2^2 \times 7^2)}$

Combine denominator

$= \frac{2^6 \times 5^4 \times 7^4}{2^{6} \times 5^4 \times 7^2}$

Cancel terms

$= 7^{4-2} = 7^2 = 49$

Final Answer: 49