How do you multiply #4y ^ { - 8} y ^ { 7} \cdot 8u ^ { 9} y \cdot 3u ^ { - 7} v ^ { 9}#?

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Answer 1 · 2017-05-31T18:03:33

See a solution process below:

First, rewrite this expression as:

#(4 * 8 * 3)(y^-8y^7y)(u^9u^-7)v^9 =>#

#96(y^-8y^7y)(u^9u^-7)v^9#

Next, use these rules of exponents to multiply the #y# terms:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))# and #a^color(red)(0) = 1#

#96(y^color(red)(-8)y^color(blue)(7)y^color(purple)(1))(u^9u^-7)v^9 =>#

#96(y^(color(red)(-8)+color(blue)(7)+color(purple)(1)))(u^9u^-7)v^9 =>#

#96(y^0)(u^9u^-7)v^9 =>#

#96(1)(u^9u^-7)v^9 =>#

#96(u^9u^-7)v^9#

Now, use this rule of exponents to multiply the #u# terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#96(u^color(red)(9)u^color(blue)(-7))v^9 =>#

#96(u^(color(red)(9)+color(blue)(-7)))v^9 =>#

#96(u^2)v^9 =>#

#96u^2v^9#