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Given [tex]x > 0[/tex], simplify [tex]625x^{40}[/tex] completely.

Answer :

In the question, we are asked to simplify 625x⁴⁰ given that x > 0. Simplifying a term with an integer power involves raising the base number to that power. In this case, we break down the base number 625 to its prime factor which is 5. The expression 625 is equivalent to 5⁴, and when we raise this to the 40th power, we apply the power of a power rule from Eq. A.8 which states that when we raise a power to a power, we multiply the exponents. Therefore, 5⁴⁰ becomes 5⁴⁰ x 4 or 5¹â¶â°. Since x is already to the power of 40, and x > 0, this simply becomes 5¹â¶â° * x⁴⁰.

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