SOLUTION: solve for x in the equation ∛(〖81〗^2 )/√(〖27〗^x )=9

Question 1195385: solve for x in the equation ∛(〖81〗^2 )/√(〖27〗^x )=9
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Rewrite using powers of 3:

Use the power to a power rule:

Rewrite using fractional exponents:

Use the power to a power rule again:

Clear fractions:

Multiply on the right (same base, so add the exponents):

The bases are the same, so the exponents are the same:

Clear fractions (multiply by the LCD, 6):

ANSWER: x = 4/9

Note that the sequence of operations could be in many different orders; or possibly grouped to perform more than one operation at a time.

I chose to take small steps in an arbitrary order....

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