Final answer:
The student's question regarding the expression (3¶-3¸)/(9´-9²) can be simplified by rewriting the bases to a single base, factoring common bases out, cancelling common terms, and simplifying to get the result -9/10.
Step-by-step explanation:
The student's question involves simplifying a mathematical expression using the properties of exponents. The expression to simplify is (3¶-3¸)/(9´-9²). To simplify this expression, recall that 9 is the same as 3², so we can rewrite the expression in terms of a single base, which is 3.
We have:
Now we can rewrite the original expression as:
(3¶ - 3¸) / (3¸ - 3´)
We see that the numerator can be simplified by factoring 3¶ out, using the rule x⁶ - x¸ = x¶(1 - x²). The denominator also can be simplified by factoring out 3´.
Thus, we simplify to:
3¶(1 - 3²) / 3´(3´ - 1)
After canceling out the common factor of 3´ we get:
3²(1 - 3²) / (3´ - 1)
Now, replacing the values again we have:
(3² - 3´) / (9² - 1)
Which simplifies to:
(9 - 81) / (81 - 1)
And finally we get:
(-72) / 80 = -9/10
Thus, the simplified result is -9/10.