Question

Find the value of $T$ to make the following equation true.
$6^4{a}^4\times T^4{b}^4=(18ab{)}^4.$

• A. $3$
• B. $3^4$
• C. $18$
• D. None of the above

Answer 1

The correct option is A $3$

$\underset{–}{\text{Need to find:}}$ Value of $T$ in $6^4{a}^4\times {\underset{–}{T}}^4{b}^4=(18ab{)}^4$

L.H.S of the given equation:
$6^4{a}^4\times T^4{b}^4$
$=(6^4\times a^4)\times (T^4\times b^4)$
$=(6a{)}^4\times (Tb{)}^4$
$=(6a\times Tb{)}^4$
$=(6Tab{)}^4$

$[\because$ Multiplication of exponents with different bases but same exponent: $x^n\times y^n=(x\times y{)}^n=(xy{)}^n]$

And, R.H.S of the given equation $(18ab{)}^4.$ So,
$(6Tab{)}^4=(18ab{)}^4$.

To make L.H.S = R.H.S, the value of $T$ should be $3$, then, L.H.S becomes $(6Tab{)}^4=(6\times 3\times ab{)}^4=(18ab{)}^4=\text{R.H.S}.$
$\therefore T=3,$ i.e., option (a.) is the correct one. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->