We are given an equation involving fractions and powers, and we are asked to enter the value of the exponent . We will need to use lots of exponent rules to answer this question!
When asked to solve for an exponent, it is often a good approach to get the equation into the form . Because the bases are equal, we can then equate the exponents too, . (Note that this will not work for bases of 1, 0, or –1.)
Our first goal is to get both sides of the equation into the form of a simple base and exponent like above. Let's start with the right side first, as it is simpler.
Now that we have the right side in the base-exponent form (base of 6), let's try to do the same for the left side. Note that we could have split 6 into factors of 2 and 3, but this would have given us more numbers to deal with rather than fewer.
Now both sides of our equation are powers of 6. We can equate the exponents to get an equation that we can solve directly for .
We have found that the value of is 1.
We enter the number 1 into the Numeric Entry box.
Watch the lessons below for more detailed explanations of the concepts tested in this question.
And don't worry, you'll be able to return to this answer from the lesson page.