Exponents on the GMAT Exam is an important topic for review. Watch the video below to learn how exponents are used on the GMAT Test.
Exponents on the GMAT Exam
Please pause this video, and answer the question before continuing. Now in this question, we want to solve this equation for k. To do this, we need to simplify the expressions on both sides of the equation. To begin, we can simplify this by applying the power of a power law, which says to multiply the two exponents to get 11 to the power of 12.
Next, we can simplify this product by applying the product law which says to add the exponents to get 11 to the power of 2 + k. Now on the right hand side, we can take one over 11 cubed, and use the negative exponent rule to rewrite this as 11 to the power of negative 3.
Now in the denominator here, we have a power of a power. So when we apply the power of a power law, we must multiple the two exponents to get 11 to the power of 8 + 4k. From here, notice that we have the quotient of two powers. So we can apply the quotient law which says to subtract the two exponents to get the following. Next, we can take this exponent, and simplify it to get 4 – 4k.
At this point, we have 11 to the power of 4 – 4k equals 11 to the power of negative 3. Since we have the same base on both sides, the following rule tells us that the two exponents must be equal. From here, we have an equation we can solve for k. When we subtract 4 from both sides, and then divide both sides by negative 4, we see that k is equal to 7 quarters. So the answer here is E.