document.write( "Question 1195385: solve for x in the equation ∛(〖81〗^2 )/√(〖27〗^x )=9 \n" ); document.write( "

Algebra.Com's Answer #827859 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"root%283%2C%2881%5E2+%29%29%2Froot%282%2C%2827%5Ex+%29%29=9\"$

\n" ); document.write( "Rewrite using powers of 3:

\n" ); document.write( " $\"root%283%2C%28%283%5E4%29%5E2+%29%29%2Froot%282%2C%28%283%5E3%29%5Ex+%29%29=3%5E2\"$

\n" ); document.write( "Use the power to a power rule: $\"%28x%5Ea%29%5Eb=x%5E%28ab%29\"$

\n" ); document.write( " $\"root%283%2C%283%5E8+%29%29%2Froot%282%2C%283%5E%283x%29+%29%29=3%5E2\"$

\n" ); document.write( "Rewrite using fractional exponents:

\n" ); document.write( " $\"%283%5E8%29%5E%281%2F3%29%2F%283%5E%283x%29%29%5E%281%2F2%29=3%5E2\"$

\n" ); document.write( "Use the power to a power rule again:
\n" ); document.write( " $\"%283%5E%288%2F3%29%29%2F%283%5E%283x%2F2%29%29=3%5E2\"$

\n" ); document.write( "Clear fractions:

\n" ); document.write( " $\"%283%5E%288%2F3%29%29=%283%5E2%29%283%5E%283x%2F2%29%29\"$

\n" ); document.write( "Multiply on the right (same base, so add the exponents):

\n" ); document.write( " $\"%283%5E%288%2F3%29%29=3%5E%282%2B3x%2F2%29\"$

\n" ); document.write( "The bases are the same, so the exponents are the same:

\n" ); document.write( " $\"8%2F3=2%2B3x%2F2\"$

\n" ); document.write( "Clear fractions (multiply by the LCD, 6):

\n" ); document.write( " $\"16=12%2B9x\"$
\n" ); document.write( " $\"9x=4\"$
\n" ); document.write( " $\"x=4%2F9\"$

\n" ); document.write( "ANSWER: x = 4/9

\n" ); document.write( "Note that the sequence of operations could be in many different orders; or possibly grouped to perform more than one operation at a time.

\n" ); document.write( "I chose to take small steps in an arbitrary order....

\n" ); document.write( " \n" ); document.write( "

\n" );