Use the rules of exponents to simplify the expression below. [ ( 3 x 2 ) ( 3 x ) 2 ( − 3 x 2 ) ( 3 x ) ] 3 \left[ \frac { \left( 3 x ^ { 2 } \right) ( 3 x ) ^ { 2 } } { \left( - 3 x ^ { 2 } \right) ( 3 x ) } \right] ^ { 3 } [ ( − 3 x 2 ) ( 3 x ) ( 3 x 2 ) ( 3 x ) 2 ] 3 A) − 26 x 7 - 26 x ^ { 7 } − 26 x 7 B) − 28 x 3 - 28 x ^ { 3 } − 28 x 3 C) − 27 x 3 - 27 x ^ { 3 } − 27 x 3 D) − 37 x 6 - 37 x ^ { 6 } − 37 x 6 E) − 17 x 8 - 17 x ^ { 8 } − 17 x 8

Question

Use the rules of exponents to simplify the expression below. [ ( 3 x 2 )  ( 3 x )  2 ( − 3 x 2 )  ( 3 x )  ] 3 \left[ \frac { \left( 3 x ^ { 2 } \right)  ( 3 x )  ^ { 2 } } { \left( - 3 x ^ { 2 } \right)  ( 3 x )  } \right] ^ { 3 } [ ( − 3 x 2 )  ( 3 x )  ( 3 x 2 )  ( 3 x )  2 ​ ] 3 A)    − 26 x 7 - 26 x ^ { 7 } − 26 x 7 B)    − 28 x 3 - 28 x ^ { 3 } − 28 x 3 C)    − 27 x 3 - 27 x ^ { 3 } − 27 x 3 D)    − 37 x 6 - 37 x ^ { 6 } − 37 x 6 E)    − 17 x 8 - 17 x ^ { 8 } − 17 x 8

Diana Betancourth · Accepted Answer

Final Answer : C, Explanation :   First, simplify the numerator and denominator separately using the rules of exponents: ( 3 x 2 ) ( 3 x ) 2 ( − 3 x 2 ) ( 3 x ) = 27 x 4 − 9 x 3 = − 3 x \frac{(3x^2)(3x)^2}{(-3x^2)(3x)} = \frac{27x^4}{-9x^3} = -3x ( − 3 x 2 ) ( 3 x ) ( 3 x 2 ) ( 3 x ) 2 ​ = − 9 x 3 27 x 4 ​ = − 3 x Now the expression becomes: ( − 3 x ) 3 = − 27 x 3 (-3x)^3 = -27x^3 ( − 3 x ) 3 = − 27 x 3 Therefore, the answer is C.

Use the rules of exponents to simplify the expression below.
$]3\left[ \frac { \left( 3 x ^ { 2 } \right) ( 3 x ) ^ { 2 } } { \left( - 3 x ^ { 2 } \right) ( 3 x ) } \right] ^ { 3 }$

A) $26 x ^ { 7 }$
B) $28 x ^ { 3 }$
C) $27 x ^ { 3 }$
D) $37 x ^ { 6 }$
E) $17 x ^ { 8 }$

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