Find the value of ( 6 7 ) − 2 \left( \frac { 6 } { 7 } \right) ^ { - 2 } ( 7 6 ) − 2 .A) − 49 36 - \frac { 49 } { 36 } − 36 49 B) 49 36 \frac { 49 } { 36 } 36 49 C) 36 49 \frac { 36 } { 49 } 49 36 D) 36 7 \frac { 36 } { 7 } 7 36 E) - 36 49 \frac { 36 } { 49 } 49 36

Question

Find the value of    ( 6 7 )  − 2 \left( \frac { 6 } { 7 } \right)  ^ { - 2 } ( 7 6 ​ )  − 2   .A)    − 49 36 - \frac { 49 } { 36 } − 36 49 ​ B)    49 36 \frac { 49 } { 36 } 36 49 ​ C)    36 49 \frac { 36 } { 49 } 49 36 ​ D)    36 7 \frac { 36 } { 7 } 7 36 ​ E)  -   36 49 \frac { 36 } { 49 } 49 36 ​

Ankur Sharma · Accepted Answer

Final Answer : B, Explanation :   Recall that   a − n = 1 a n a^{-n}=\frac{1}{a^n} a − n = a n 1 ​   for any real number   a a a   (except 0) and positive integer   n n n  . Thus, we have   ( 6 7 ) − 2 = ( 7 6 ) 2 = 49 36 . \left( \frac { 6 } { 7 } ight) ^ { - 2 } = \left(\frac{7}{6}ight)^2 = \frac{49}{36}. ( 7 6 ​ ) − 2 = ( 6 7 ​ ) 2 = 36 49 ​ .   Therefore, the answer is $\boxed{	ext{(B)}}.$

Find the value of $−2\left( \frac { 6 } { 7 } \right) ^ { - 2 }$ .

A) $\frac { 49 } { 36 }$
B) $4936\frac { 49 } { 36 }$
C) $3649\frac { 36 } { 49 }$
D) $367\frac { 36 } { 7 }$
E) - $3649\frac { 36 } { 49 }$

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Find the value of (67) −2\left( \frac { 6 } { 7 } \right) ^ { - 2 }(76​) −2 .A) −4936- \frac { 49 } { 36 }−3649​ B) 4936\frac { 49 } { 36 }3649​ C) 3649\frac { 36 } { 49 }4936​ D) 367\frac { 36 } { 7 }736​ E) - 3649\frac { 36 } { 49 }4936​

Definitions

Learning Objectives

Learning Objectives

Related questions

Find the value of $−2\left( \frac { 6 } { 7 } \right) ^ { - 2 }$ .

A) $\frac { 49 } { 36 }$
B) $4936\frac { 49 } { 36 }$
C) $3649\frac { 36 } { 49 }$
D) $367\frac { 36 } { 7 }$
E) - $3649\frac { 36 } { 49 }$