Question: Which of the following is equal to \(5^{17}\) * \(4^{9}\)?
- 2 * \(10^{13}\)
- 2* \(10^{17}\)
- 2* \(10^{20}\)
- 2* \(10^{26}\)
- 2* \(10^{36}\)
“Which of the following is equal to \(5^{17}\) * \(4^{9}\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
This question has only one approach.
Given to us a number \(5^{17}\) * \(4^{9}\). It is asked which of the numbers from the options are equal to the given number.
It should be noted that the given number to us is in the powers of 5 and 4. But in all the options the number is in the powers of 10.
Therefore we had to convert the given number into the powers of 10
Firstly, in order to make the number in the powers of 10 we had to find the factors of 10.
We can write 10 = 5 * 2
So let us take 10 to the power of x
\(10^x\) = \((5*2)^x\) =\(5^x*2^x\)
In general,
\((x)^n\)*\((y)^n\) = \((xy)^n\).
Therefore we got the power of 10 in the form of 5 and 2
Now in the given number we already have 5^17
4^9 needs to be converted.
It should be noted that we can write \(4^9\) as \((2^2)^9\)
\(4^9\) = \((2^2)^9\) = \(2^{2*9}\) = \(2^{18}\)
We get \(4^9\) = \(2^{18}\)
Now putting this in the number we get
\(5^{17}\)*\(2^{18}\)
Taking 2 common to make the powers equal we get,
\(5^{17}\) * \(2^{17}*2^1\) = 2 * (\(5^{17}\)*\(2^{17}\)) = 2 * \((5*2)^{17}\) = 2 *\(10^{17}\).
Therefore the correct answer is 2 * \(10^{17}\)
Correct Answer: B
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