Respuesta :
Answer:
[tex]\sqrt[4]{7.5^{4} }[/tex]
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]
Given
[tex]7.5^{1.25}[/tex]
= [tex]7.5^{\frac{5}{4} }[/tex]
= [tex]\sqrt[4]{7.5^{4} }[/tex]
[tex]\sqrt[4]{7.5^{5} }[/tex] is the radical for [tex]7.5^{1.25}[/tex].
What are exponent rules?
Exponent rules, which are also known as the 'laws of exponents' or the 'properties of exponents' make the process of simplifying expressions involving exponents easier. These rules are helpful to simplify the expressions that have decimals, fractions, irrational numbers, and negative integers as their exponents.
Given
[tex]7.5^{1.25}[/tex]
We can write 1.25 is [tex]\frac{5}{4}[/tex]
[tex]7.5^{\frac{5}{4} }[/tex]
Using the rule of exponents/radicals
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex]
[tex]7.5^{\frac{5}{4} }[/tex] = [tex]\sqrt[4]{7.5^{5} }[/tex]
[tex]\sqrt[4]{7.5^{5} }[/tex] is the radical for [tex]7.5^{1.25}[/tex].
Find out more information about rule of exponents here
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