document.write( "Question 120491: (-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14.
\n" ); document.write( "What I don't understand is, how did the negative sign shift to the 5 only? Please explain. Thanks \n" ); document.write( "
Algebra.Com's Answer #88316 by stanbon(75887)\"\" \"About 
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(-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14.
\n" ); document.write( "What I don't understand is, how did the negative sign shift to the 5 only? Please explain.
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\n" ); document.write( "(-1) raised to an even power is 1
\n" ); document.write( "(-1) raised to an odd power is negative
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\n" ); document.write( "Your problem:
\n" ); document.write( "(-5a^2)(-5a^3)^4
\n" ); document.write( "The -5 in the 1st factor is raised to the power one which is odd
\n" ); document.write( "so the negative survives.
\n" ); document.write( "The -5 in the 2nd factor is raised to the power 4 which is even
\n" ); document.write( "so the negative becomes positive.
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\n" ); document.write( "(-5a^2)(-5a^3)^4
\n" ); document.write( "= (-5a^2)[(-5)^4(a^3)^4]
\n" ); document.write( "= (-5)(a^2)(-5)^4(a^12)
\n" ); document.write( "= (-5)^5(a^14)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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