select the correct answer.\nwhich expression is equivalent to ( 4 x ^ { 2 } sqrt { 5 x ^ { 4 } } cdot 3 sqrt…

select the correct answer.\nwhich expression is equivalent to ( 4 x ^ { 2 } sqrt { 5 x ^ { 4 } } cdot 3 sqrt { 5 x ^ { 8 } } ), if ( x \neq 0 )?\na. ( 12 x ^ { 10 } sqrt { 5 } )\nb. ( 60 x ^ { 8 } )\nc. ( 35 x ^ { 18 } )\nd. ( 7 x ^ { 10 } sqrt { 5 } )

select the correct answer.\nwhich expression is equivalent to ( 4 x ^ { 2 } sqrt { 5 x ^ { 4 } } cdot 3 sqrt { 5 x ^ { 8 } } ), if ( x \neq 0 )?\na. ( 12 x ^ { 10 } sqrt { 5 } )\nb. ( 60 x ^ { 8 } )\nc. ( 35 x ^ { 18 } )\nd. ( 7 x ^ { 10 } sqrt { 5 } )

Answer

Explanation:

Step1: Multiply the coefficients

Multiply (4) and (3): (4\times3 = 12)

Step2: Use the property (\sqrt{a}\cdot\sqrt{b}=\sqrt{ab})

Multiply (\sqrt{5x^{4}}) and (\sqrt{5x^{8}}): (\sqrt{5x^{4}\cdot5x^{8}}=\sqrt{25x^{12}}) Since (\sqrt{25x^{12}} = 5x^{6}) (because (\sqrt{25}=5) and (\sqrt{x^{12}}=x^{6}) for (x\neq0))

Step3: Multiply the (x -)terms

Multiply (x^{2}) (from (4x^{2})) with (x^{6}) (from (\sqrt{25x^{12}})) using the rule (a^{m}\cdot a^{n}=a^{m + n}). So (x^{2}\cdot x^{6}=x^{2 + 6}=x^{8})

Step4: Combine all parts

Multiply the coefficient ((12)) with the (x -)term ((x^{8})) and the result from the square - root multiplication ((5)): (12\times5\times x^{8}=60x^{8})

Answer:

B. (60x^{8})