To simplify this expression, we can first rewrite the exponents as fractions:
2.5^(1/7) 2^(2/7) 10^(6/7)
Next, we can use the property of exponents that states a^(m/n) = (a^(1/n))^m:
= (2.5^(1/7) 2^(2/7) 10^(6/7))= ((2.5 2^2 10^6)^(1/7))
Now, let's simplify the inner part of the parentheses:
= (2.5 4 10^6)^(1/7)= (10 * 10^6)^(1/7) = (10^7)^(1/7)
Since raising a number to the power of 1/n is equivalent to taking the n-th root of the number, we have:
= 10
Therefore, 2.5^(1/7) 2^(2/7) 10^(6/7) simplifies to 10.
To simplify this expression, we can first rewrite the exponents as fractions:
2.5^(1/7) 2^(2/7) 10^(6/7)
Next, we can use the property of exponents that states a^(m/n) = (a^(1/n))^m:
= (2.5^(1/7) 2^(2/7) 10^(6/7))
= ((2.5 2^2 10^6)^(1/7))
Now, let's simplify the inner part of the parentheses:
= (2.5 4 10^6)^(1/7)
= (10 * 10^6)^(1/7) = (10^7)^(1/7)
Since raising a number to the power of 1/n is equivalent to taking the n-th root of the number, we have:
= 10
Therefore, 2.5^(1/7) 2^(2/7) 10^(6/7) simplifies to 10.