The expression ∛(a)⁷ raised to a single rational exponent is [tex]a^{\frac{7}{3} }[/tex] .
A rational number is one that can be defined as the ratio or fraction a/b of two numbers, where a and b are the numerator and denominator, respectively. Here the integer numbers a and b are co prime numbers.
For example 8/7 is a rational number and all integers are rational numbers.
Any combination of terms that have undergone operations like multiplication,addition, subtraction, division is known as an algebraic expression.
it is given that the expression is of the form ∛(a)⁷ .
We know that the n-th root of a variable x ([tex]\sqrt[n]{x}[/tex]) can also be written as
[tex]x^{\frac{1}{n} }[/tex].
Therefore ∛(a) can be written as [tex]a^{\frac{1}{3} }[/tex] . Now the complete expression is ∛(a)⁷.
So [tex](a^{\frac{1}{3} })^7=a^{\frac{7}{3} }[/tex] and we know that 7/3 is a rational number.
Therefore the expression can be written as [tex]a^{\frac{7}{3} }[/tex] using rational exponents.
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