Question

help please somebody ​

Answer 1

$\pink\bigstar$ Question:

• $[ { { (\frac{5}{2}) }^{ - 2} }]^{( - 3)} \times ( { \frac{ - 1}{9} })^{( - 2)} \times \frac{1}{25}$

$\pink\bigstar$ Answer:

$\frac{50625}{64}$

$\pink\bigstar$ Given:

• $[ { { (\frac{5}{2}) }^{ - 2} }]^{( - 3)} \times ( { \frac{ - 1}{9} })^{( - 2)} \times \frac{1}{25}$

$\pink\bigstar$To find:

The value of :

$[ { { (\frac{5}{2}) }^{ - 2} }]^{( - 3)} \times ( { \frac{ - 1}{9} })^{( - 2)} \times \frac{1}{25}$

$\pink\bigstar$ Solution:

$[ { { (\frac{5}{2}) }^{ - 2} }]^{( - 3)} \times ( { \frac{ - 1}{9} })^{( - 2)} \times \frac{1}{25}$

$= { \frac{5}{2} }^{( - 2)( - 3)} \times { ( \frac{ - 9}{1} )}^{2} \times \frac{1}{25}$

$( \rm \: using \: { {a}^{m} }^{n} = {a}^{mn} \: \: )$

$( \rm \: using \: \: {a}^{( - 1)} = \frac{1}{a} )$

$= { (\frac{5}{2} )}^{6} \times {( - 9)}^{2} \times {5}^{( - 2)}$

$( \rm \: using \: \frac{1}{a} = {a}^{ - 1} )$

$= \frac{15625}{64} \times \frac{1}{25} \times 81$

$= \frac{ \cancel{15625}}{64} \times \frac{1}{ \cancel{25}} \times 81$

$= \frac{625}{64} \times 81$

$= \frac{50625}{64}$

$\therefore$ answer is $\frac{50625}{64}$

$\pink\bigstar$Some few laws of exponents:

• $\rm \: {a}^{( - 1)} = \frac{1}{a}$
• $\rm \: { {a}^{m}}^{n} = a^{mn}$
• $\rm \: \frac{{a}^{m}}{{a}^{n} } = \frac{{a^{m}}}{{a^{n}}}$
• $\rm \frac{1}{a} = {a}^{( - 1)}$