Question

The value of $\frac{6^{12}\times (35{)}^{28}\times (15{)}^{16}}{(14{)}^{12}\times (21{)}^{11}\times 5^{28}}$ is _____ .

• A. $2^6\times 3^{16}\times 5^{12}$
• B. $3^{17}\times 5^{16}\times 7^5$
• C. $2^5\times 5^{16}\times 7^{12}$
• D. $2^7\times 3^{17}\times 7^5$

Answer 1

The correct option is B $3^{17}\times 5^{16}\times 7^5$

$6=2\times 3$

$35=5\times 7$

$15=3\times 5$

$14=2\times 7$

$21=3\times 7$

$\Rightarrow \frac{6^{12}\times (35{)}^{28}\times (15{)}^{16}}{(14{)}^{12}\times (21{)}^{11}\times 5^{28}}=\frac{2^{12}\times 3^{28}\times 5^{44}\times 7^{28}}{2^{12}\times 3^{11}\times 5^{28}\times 7^{23}}$

$=3^{17}\times 5^{16}\times 7^5$