Question

❤❤❤Hi frndzz❤❤❤

Simplify using laws of exponents:
$\frac{ {90}^{3} \times \sqrt[7]{128} \times 1331 }{ {11}^{4} \times 512 \times \sqrt[4]{729} }$

Answer 1

${Answer :-}$

Here, we have,

[(90)^3 * (128)^1/7 * 1331] / [ (11)^4 * 512 * (729)^1/4

= [ ( 9 * 10)^3 * ( 2^7)^1/7 * (11)^3] / [ (11)^4 * ( 2^9) * ( 3^6)^1/4].
{ using,(ab) ^n = a^n * b^n}

= [ ( 3^2 * 2 * 5)^3 * 2^(7*1/7) * (11)^3] / [ (11)^4 * 2^9 * 3^(6*1/4)].

= [ 3^6 * 2^3 * 5^3 *2^1 * 11^3] / [ 11^4 * 2^9 * 3^3/2 * 1].
{ using, (a^n)^m = a^(mn)}

= [ 3^6 * 2^4 * 5^3 * 11^3] / [ 11^4 * 2^9 * 3^3/2 * 5^0].
{using, a^0 = 1}

= 3^(6 - 3/2) * 2^(4 - 9) * 11^(3-4) * 5^(3 - 0).
{ using, (a^m)/ (a^n) = a^(m-n)}

= 3^(9/2) * 2^(-5) * 11^(-1) * 5^(3)

= [ 3^(9/2) * 5^(3)] / [ 2^(5) * 11^(1)].
{using, a^(-1) = 1/a}

Hope this helps,.

If helps, please mark it as brainliest ^_^

Answer 2

$the \: answer \: is \: in \: the \: picture \\ \\ please \: mark \: as \: brainliest$