Respuesta :
we are given
[tex] \sqrt[3]{d} *\sqrt[3]{d}*\sqrt[3]{d} [/tex]
we can use property of exponents
[tex] \sqrt[n]{a}*\sqrt[n]{b} *\sqrt[n]{c}=\sqrt[n]{a*b*c} [/tex]
so, we can write it as
[tex] \sqrt[3]{d} *\sqrt[3]{d}*\sqrt[3]{d}=\sqrt[3]{d*d*d} [/tex]
[tex] \sqrt[3]{d} *\sqrt[3]{d}*\sqrt[3]{d}=\sqrt[3]{d^3} [/tex]
we can simplify it
and we get
[tex] \sqrt[3]{d} *\sqrt[3]{d}*\sqrt[3]{d}=d [/tex]................Answer
The product of the given expression [tex]\sqrt[3]{d} \sqrt[3]{d} \sqrt[3]{d}[/tex] will be option A; d.
What are some basic properties of exponentiation?
If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
we are given expression as;
[tex]\sqrt[3]{d} \sqrt[3]{d} \sqrt[3]{d}[/tex]
we can use property of exponents,
[tex]\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{c} = \sqrt[3]{abc}[/tex]
so, we can write it as
[tex]\sqrt[3]{d} \sqrt[3]{d} \sqrt[3]{d} = \sqrt[3]{d \times d\times d} \\\\\sqrt[3]{d} \sqrt[3]{d} \sqrt[3]{d} = \sqrt[3]{d ^3}\\\\\sqrt[3]{d} \sqrt[3]{d} \sqrt[3]{d} = d[/tex]
we can simplify it and we get the answer as d.
Therefore, the product of the given expression [tex]\sqrt[3]{d} \sqrt[3]{d} \sqrt[3]{d}[/tex] will be option A; d.
Learn more about exponentiation here:
https://brainly.com/question/26938318
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