SOLUTION: Can help me solve this problem...instructions...what expression raised to the fourth power is 81x^12y^8z^16?

Question 71368: Can help me solve this problem...instructions...what expression raised to the fourth power is 81x^12y^8z^16?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
what expression raised to the fourth power is
.
Notice some things here ...
.
and
and
and finally

.
The last three of these (for the letter variables) show the power rule ... that if you raise
a term with an exponent to a power the result can be found by multiplying the power by
the exponent. In all of these cases the power 4 multiplies the exponent of the variable,
and the result is that it gets you back to the corresponding term of the original
problem.
.
Now notice the power of 4 is common to every term. We can pull it and raise the entire
product to the power of 4. This results in:
.

.
From this you can see that the term that when raised to the fourth power gives you the
original term in the problem is
.
Hope this helps you to become a little more familiar with the properties of exponents
and especially how to raise variables with exponents to another power.

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