document.write( "Question 75667: Use the five properties of exponents to simplify each of the following expressions.
\n" ); document.write( "(y^5)^3(y^3)^2 / (y^4)4
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #54354 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28%28y%5E5%29%5E3%28y%5E3%29%5E2%29%2F%28y%5E4%29%5E4\"$
\n" ); document.write( "When you raise a base with an exponent to an exponent, you multiply the exponents:
\n" ); document.write( "in other words,
\n" ); document.write( " $\"%28x%5Ey%29%5Ez=x%5E%28y%2Az%29\"$ So in our problem $\"%28y%5E5%29%5E3=y%5E%283%2A5%29=y%5E15\"$ and we do this for every exponent raised to an exponent
\n" ); document.write( " $\"%28%28y%5E%285%2A3%29%29%28y%5E%283%2A2%29%29%29%2F%28y%5E%284%2A4%29%29\"$
\n" ); document.write( " $\"%28%28y%5E%2815%29%29%28y%5E%286%29%29%29%2F%28y%5E%2816%29%29\"$
\n" ); document.write( "Now when you are multiplying like bases with exponents, you add the exponents ie $\"x%5E2%2Ax%5E3=x%5E%282%2B3%29=x%5E5\"$ . So it becomes:
\n" ); document.write( " $\"%28%28y%5E%2815%2B6%29%29%29%2F%28y%5E%2816%29%29\"$
\n" ); document.write( " $\"%28%28y%5E%2821%29%29%29%2F%28y%5E%2816%29%29\"$
\n" ); document.write( "When you divide like bases with exponents you subtract the exponents ie $\"x%5E3%2Fx%5E2=x%5E%283-2%29=x%5E1=x\"$
\n" ); document.write( " $\"y%5E%2821-16%29\"$
\n" ); document.write( " $\"y%5E%285%29\"$
\n" ); document.write( "So the whole thing reduces down to $\"y%5E5\"$ in other words
\n" ); document.write( " $\"%28%28y%5E5%29%5E3%28y%5E3%29%5E2%29%2F%28y%5E4%29%5E4=y%5E5\"$ \n" ); document.write( "

\n" );