Question

Which of the following option is equal to ${16}^3{a}^{12}\times {125}^4{b}^{12}?$

• A. $(10ab{)}^{12}$
• B. $10(ab{)}^{12}$
• C. $(10{)}^{12}ab$
• D. None of the above

Answer 1

The correct option is A $(10ab{)}^{12}$

$\underset{–}{\text{Need to simplify:}}{16}^3{a}^{12}\times {125}^4{b}^{12}$

${16}^3{a}^{12}\times {125}^4{b}^{12}$
$=(2^4{)}^3{a}^{12}\times (5^3{)}^4{b}^{12}$
[ As $16=2\times 2\times 2\times 2=2^4$ and $125=5\times 5\times 5=5^3$ ]

$=2^{4\times 3}{a}^{12}\times 5^{3\times 4}{b}^{12}$
[ As $(a^m{)}^n=a^{m\times n}$ ]

$=2^{12}{a}^{12}\times 5^{12}{b}^{12}$
$=2^{12}\times a^{12}\times 5^{12}\times b^{12}$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> [ Multiplying exponents with different bases but same exponent: $c^n\times d^n\times p^n\times q^n=(c\times d\times p\times q{)}^n$ ]

$=(2\times a\times 5\times b{)}^{12}$
$=(2\times 5\times a\times b{)}^{12}$
$\Rightarrow {16}^3{a}^{12}\times {125}^4{b}^{12}=(10ab{)}^{12}$

Therefore, option (a.) is the correct one.