Question

Evaluate: $\frac{{11}^{12}\times {121}^{13}}{{121}^{12}\times {11}^{13}}$

• A. $11$
• B. ${11}^{25}$
• C. ${11}^0$ or $1$
• D. ${11}^0+{121}^0$

Answer 1

The correct option is A $11$

$\frac{{11}^{12}\times {121}^{13}}{{121}^{12}\times {11}^{13}}=\frac{{11}^{12}\times ({11}^2{)}^{13}}{({11}^2{)}^{12}\times {11}^{13}}$

$=\frac{{11}^{12}\times (11{)}^{2\times 13}}{(11{)}^{2\times 12}\times {11}^{13}}$ $($Using properties of exponent, that is $(a^m{)}^n=a^{m\times n})$

$=\frac{{11}^{12}\times {11}^{26}}{{11}^{24}\times {11}^{13}}$

$=\frac{(11{)}^{12+26}}{(11{)}^{24+13}}$ $($Using properties of exponent, that is $a^m\times a^n=a^{m+n})$

$=\frac{{11}^{38}}{{11}^{37}}$
$=(11{)}^{38-37}$ $($Using properties of exponent, that is $a^m÷a^n=a^{m-n})$
$={11}^1=11$