what number has the prime factorization of 2 to the 6th power and 5 to the 6th power
Use your calculator to find
26×56.
Since they are both raised to the 6th power, if you are interested in mental calculations, you can apply the law of exponents and multiply the two bases before raising to the given power.
2^6 =
64
5^6= 15625
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To find the number with the given prime factorization, we need to multiply the base numbers: 2 and 5, by their respective exponents: 6.
The base number 2 raised to the 6th power is expressed as 2^6, which means multiplying 2 by itself 6 times: 2 x 2 x 2 x 2 x 2 x 2 = 64.
Similarly, the base number 5 raised to the 6th power is expressed as 5^6, which means multiplying 5 by itself 6 times: 5 x 5 x 5 x 5 x 5 x 5 = 15625.
Now, to find the number that has the prime factorization of 2^6 x 5^6, we simply multiply the results: 64 x 15625 = 1,000,000.
Therefore, the number with the prime factorization of 2 to the 6th power and 5 to the 6th power is 1,000,000.