Question

Simplify (243/32)^-4/5

Answer 1

Given, (243/32)^-4/5 

= (3^5/2^5)^-4/5 

= (3/2)^-4 

= 16/81

Answer 2

$\bf \red{\left({ \frac{243}{32} } \right)^{ - \frac{4}{5} } = \frac{16}{81} }$

Step-by-step explanation:

Given:

• $\left({ \frac{243}{32} } \right)^{ - \frac{4}{5} }$

To find:

• Simply the expression.

Solution:

Identify to be used:

1. $\left({ \frac{a}{b} } \right)^{ - \frac{m}{n} } = \left({ \frac{b}{a} } \right)^{ \frac{m}{n} }$
2. $( { {a}^{m} })^{ \frac{1}{m} } = a$

Step 1:

Write 243 and 32 in powers of 3 and 2 respectively.

$243 = {3}^{5}$

and

$32 = {2}^{5}$

So,

$\left({ \frac{243}{32} } \right)^{ - \frac{4}{5} } = \left({ \frac{32}{243} } \right)^{\frac{4}{5} }$

or

$\left({ \frac{32}{243} } \right)^{\frac{4}{5} } = \left({ \frac{ {(2)}^{5} }{ {(3)}^{5} } } \right)^{\frac{4}{5} }$

or

Apply Identity 2.

$\left({ \frac{ {(2)}^{5} }{ {(3)}^{5} } } \right)^{\frac{4}{5} } =\left({ \frac{ {(2)}^{5 \times \frac{1}{5} } }{ {(3)}^{5 \times \frac{1}{5} } } } \right)^{4}$

or

$\left({ \frac{ {(2)}^{5 \times \frac{1}{5} } }{ {(3)}^{5 \times \frac{1}{5} } } } \right)^{4} = \left({ \frac{2}{3} } \right)^{4}$

Step 2:

Simply the last expression.

$\left({ \frac{2}{3} } \right)^{4} = \frac{ {2}^{4} }{ {3}^{4} }$

or

$\frac{ {2}^{4} }{ {3}^{4} } = \frac{16}{81}$

Thus,

$\bf \left({ \frac{243}{32} } \right)^{ - \frac{4}{5} } = \frac{16}{81}$

Learn more:

1) simplify 12⁴×9³×4/6³×8²×27

https://brainly.in/question/2797724

2) evaluate (343/1331)1/3

https://brainly.in/question/10672485

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