How do you multiply (5a ^ { 3} b ) ^ { 2} \cdot ( 2a ^ { 3} b ^ { 4} )?

1 Answer
Mar 23, 2017

=50a^9b^6

Explanation:

In this exercise we have to use some properties of powers:
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color(green)((axxb)^n=a^nxxb^n
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Power of a power
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color(blue)((a^m)^n=a^(mxxn)
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Multiplication of powers with same base:
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color(red)(a^bxxa^c=a^(b+c)
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(5a^3b)^2.(2a^3b^4)
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=color(green)(5^2xx(a^3)^2xxb^2).2xxa^3xxb^4
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=25xxcolor(blue)(a^(3xx2))xxb^2xx2xxa^3xxb^4
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=25xxcolor(blue)(a^6)xxb^2xx2xxa^3xxb^4
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=25xx2xxa^6xxa^3xxb^2xxb^4
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=50xxcolor(red)(a^(6+3))xxcolor(red)(b^(2+4))
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=50xxcolor(red)(a^9)xxcolor(red)(b^6)
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=50a^9b^6