simplify:-
a) {(5)^-1×(4)^-1}^2
b) {(3)-1÷(4)^-1}^3
c) {(5)^-1÷(3)^-1}^-1×(2)^-1
d) {(3)^2+(2)^2-(4)^2}÷(3/2)^2
e) {(3)^-5×(10)^-5×125}÷{(5)^7×(6)^-5}
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simplify:-
a) {(5)^-1×(4)^-1}^2
b) {(3)-1÷(4)^-1}^3
c) {(5)^-1÷(3)^-1}^-1×(2)^-1
d) {(3)^2+(2)^2-(4)^2}÷(3/2)^2
e) {(3)^-5×(10)^-5×125}÷{(5)^7×(6)^-5}
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Verified answer
Given:
a) {(5)^-1×(4)^-1}^2
b) {(3)-1÷(4)^-1}^3
c) {(5)^-1÷(3)^-1}^-1×(2)^-1
d) {(3)^2+(2)^2-(4)^2}÷(3/2)^2
To find:
we need to simplify the given expressions
Solution:
To solve this problem, we just need to know a simple formula
[tex] \frac{1}{ {a}^{m} } = {a}^{ - m} [/tex]
a)
[tex] = ( \frac{1}{5} \times \frac{1}{4} )^{2} [/tex]
[tex] = ( \frac{1}{20} )^{2} [/tex]
[tex] = \frac{1}{400} [/tex]
b)
[tex] = ( \frac{1}{3} \div \frac{1}{4} )^{3} [/tex]
[tex]( \frac{ \frac{1}{3} }{ \frac{1}{4} } )^{3} [/tex]
[tex] = ( \frac{4}{3} )^{3} [/tex]
[tex] = \frac{64}{27} [/tex]
c)
[tex] = ( \frac{1}{5} \div \frac{1}{3} ) ^{ - 1} \times \frac{1}{2} [/tex]
[tex] (\frac{ \frac{1}{5} }{ \frac{1}{3} } )^{ - 1} \times \frac{1}{2} [/tex]
[tex] = ( \frac{5}{3} ) \times \frac{1}{2} [/tex]
[tex] = \frac{5}{6} [/tex]
d)
[tex] = (9 + 4 - 16) \div \frac{9}{4} [/tex]
[tex]=( - 3) \div \frac{9}{4} [/tex]
[tex] =\frac{ - 3}{ \frac{9}{4} } [/tex]
[tex] = \frac{ - 12}{9} [/tex]
[tex] = \frac{ - 4}{3} [/tex]
Step-by-step explanation:
[tex] {4 }^{2} + {3}^{2} = 25[/tex]