Simplify the expression ( s t ) 8 ( s 6 t ) 2 ( s t ) ^ { 8 } \left( s ^ { 6 } t \right) ^ { 2 } ( s t ) 8 ( s 6 t ) 2 .A) s 44 t 32 s ^ { 44 } t ^ { 32 } s 44 t 32 B) s 37 t 16 s ^ { 37 } t ^ { 16 } s 37 t 16 C) s 16 t 10 s ^ { 16 } t ^ { 10 } s 16 t 10 D) s 96 t 16 s ^ { 96 } t ^ { 16 } s 96 t 16 E) s 20 t 10 s ^ { 20 } t ^ { 10 } s 20 t 10

Question

Simplify the expression   ( s t )  8 ( s 6 t )  2 ( s t )  ^ { 8 } \left( s ^ { 6 } t \right)  ^ { 2 } ( s t )  8 ( s 6 t )  2   .A)    s 44 t 32 s ^ { 44 } t ^ { 32 } s 44 t 32 B)    s 37 t 16 s ^ { 37 } t ^ { 16 } s 37 t 16 C)    s 16 t 10 s ^ { 16 } t ^ { 10 } s 16 t 10 D)    s 96 t 16 s ^ { 96 } t ^ { 16 } s 96 t 16 E)    s 20 t 10 s ^ { 20 } t ^ { 10 } s 20 t 10

Zybrea Knight · Accepted Answer

Final Answer : E, Explanation :   Using the properties of exponents, the expression simplifies to   s 16 t 8 ⋅ s 12 t 2 = s 16 + 12 t 8 + 2 = s 28 t 10 s^{16}t^8 \cdot s^{12}t^2 = s^{16+12}t^{8+2} = s^{28}t^{10} s 16 t 8 ⋅ s 12 t 2 = s 16 + 12 t 8 + 2 = s 28 t 10  , which is not listed among the options provided. Therefore, it seems there might be a mistake in the transcription of the options or in the calculation. Based on the correct calculation, none of the provided options match.

Simplify the expression $\left( s ^ { 6 } t \right) ^ { 2 }$ .

A) $s ^ { 44 } t ^ { 32 }$
B) $s ^ { 37 } t ^ { 16 }$
C) $s ^ { 16 } t ^ { 10 }$
D) $s ^ { 96 } t ^ { 16 }$
E) $s ^ { 20 } t ^ { 10 }$

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Learning Objectives

Related questions

Simplify the expression (st) 8(s6t) 2( s t ) ^ { 8 } \left( s ^ { 6 } t \right) ^ { 2 }(st) 8(s6t) 2 .A) s44t32s ^ { 44 } t ^ { 32 }s44t32 B) s37t16s ^ { 37 } t ^ { 16 }s37t16 C) s16t10s ^ { 16 } t ^ { 10 }s16t10 D) s96t16s ^ { 96 } t ^ { 16 }s96t16 E) s20t10s ^ { 20 } t ^ { 10 }s20t10

Definitions

Learning Objectives

Learning Objectives

Related questions

Simplify the expression $\left( s ^ { 6 } t \right) ^ { 2 }$ .

A) $s ^ { 44 } t ^ { 32 }$
B) $s ^ { 37 } t ^ { 16 }$
C) $s ^ { 16 } t ^ { 10 }$
D) $s ^ { 96 } t ^ { 16 }$
E) $s ^ { 20 } t ^ { 10 }$