Question

simplify
pls do with steps​

Answer 1

Answer:

= 1

Step-by-step explanation:

$\implies \sf \bigg( \dfrac{81}{16} \bigg)^{\dfrac{-3}{4}}\times \bigg[ \bigg( \dfrac{25}{9} \bigg)^{\dfrac{-3}{2}} \div \bigg( \dfrac{5}{2} \bigg)^{-3} \bigg]$

$\implies \sf \bigg( \dfrac{81}{16} \bigg)^{\dfrac{-3}{4}}\times \bigg[ \bigg( \dfrac{25}{9} \bigg)^{\dfrac{-3}{2}} \div \bigg( \dfrac{2}{5} \bigg)^{3} \bigg]$

$\implies \sf \bigg( \dfrac{16}{81} \bigg)^{\dfrac{3}{4}} \times \bigg[ \bigg( \dfrac{9}{25} \bigg)^{\dfrac{3}{2}} \div \dfrac{2^3}{5^3} \bigg]$

$\implies \sf \dfrac{16^{\dfrac{3}{4}}}{81^{\dfrac{3}{4}}} \times \bigg[ \dfrac{9^{\dfrac{3}{2}}}{25^{\dfrac{3}{2}}} \times \dfrac{5^3}{2^3} \bigg]$

$\implies \sf \dfrac{2^3}{3^3} \times \bigg( \dfrac{3^3}{5^3} \times \dfrac{5^3}{8} \bigg)$

$\implies \sf \dfrac{2^3}{3^3} \bigg( 27 \times \dfrac{1}{8} \bigg)$

$\implies \sf \dfrac{2^3}{3^3} \times \dfrac{27}{8}$

$\implies \sf \dfrac{2^3}{3^3} \times \dfrac{3^3}{2^3}$

$\implies \sf \dfrac{\cancel{2^3}}{\cancel{3^3}} \times \dfrac{\cancel{3^3}}{\cancel{2^3}}$

$\implies \sf 1$

Answer 2

Step-by-step explanation:

Question:-

$\bigg( \frac{81}{16} \bigg)^{ - 3/4 } \times \left\{ \bigg( \frac{25}{9} \bigg)^{ - 3/2} \div \bigg( \frac{5}{2} \bigg) ^{ - 3} \right\}$

What to do:

To simplify.

Solution:-

Let's solve the given problem

We have,

$\bigg( \frac{81}{16} \bigg)^{ - 3/4 } \times \left\{ \bigg( \frac{25}{9} \bigg)^{ - 3/2} \div \bigg( \frac{5}{2} \bigg) ^{ - 3} \right\}$

$⟹ \bigg( \frac{16}{81} \bigg)^{ 3/4 } \times \left\{ \bigg( \frac{9}{25} \bigg)^{3/2} \div \bigg( \frac{2}{5} \bigg) ^{ 3} \right\}$

$⟹ \bigg( \frac{ {2}^{4} }{ {3}^{4} } \bigg)^{ 3/4 } \times \left\{ \bigg( \frac{ {3}^{2} }{ {5}^{2} } \bigg)^{3/2} \div \bigg( \frac{2}{5} \bigg) ^{ 3} \right\}$

$⟹ \bigg( \frac{2}{3} \bigg)^{ \cancel{4 }\times 3/ \cancel{4} } \times \left\{ \bigg( \frac{3}{5} \bigg)^{ \cancel{2 }\times 3/ \cancel{2}} \div \bigg( \frac{2}{5} \bigg) ^{ 3} \right\}$

$⟹ \bigg( \frac{2}{3} \bigg)^{ 3 } \times \left\{ \bigg( \frac{3}{5} \bigg)^{3} \times \bigg( \frac{5}{2} \bigg) ^{ 3} \right\}$

$⟹ \bigg( \frac{2}{3} \bigg)^{ 3 } \times \bigg( \frac{ {3}^{3} } { \cancel{ {5}^{3}} } \times \frac{ \cancel{{5}^{3}} }{ {2}^{3} } \bigg)$

$⟹ \bigg( \frac{2}{3} \bigg)^{ 3 } \times \bigg( \frac{3}{2} \bigg)^{ 3 }$

$⟹ \frac{ \cancel{{2}^{3}} }{ \cancel{{3}^{3} }} \times \frac{ \cancel{ {3}^{3}} }{ \cancel{{2}^{3}} }$

$⟹1.Ans$

Answer:-

• 1

More information:-

Low of Integral Exponents

For any two real numbers a and b, a, b ≠ 0, and for any two positive integers, m and n

➲ If a be any non - zero rational number, then

a^0 = 1

➲ If a be any non - zero rational number and m,n be integer, then

(a^m)^n = a^mn

➲ If a be any non - zero rational number and m be any positive integer, then

a^-m = 1/a^m

➲ If a/b is a rational number and m is a positive integer, then

(a/b)^m = a^m/b^m

➲ For any Integers m and n and any rational number a, a ≠ 0

a^m × a^n = a^m+n

➲ For any Integers m and n for non - zero rational number a,

a^m ÷ a^n = a^m-n

➲ If a and b are non - zero rational numbers and m is any integer, then

(a+b)^m = a^m × b^m

I hope it's help you...☺

:)