Answer :
Answer:
the answer is b: StartFraction 1 Over x Superscript 21 Baseline y Superscript 12 Baseline EndFraction
Step-by-step explanation:
The simplified form of the expression [(x^(-3)y^2) / (x^4 y^6)]^3 is given by: Option B: 1/(x^(21) y^(12) )
What is simplification of an expression?
Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
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]
The considered expression is:
[tex]\left(\dfrac{x^{-3} y^2}{x^4 y^6}\right)^3[/tex]
Firstly, we will simplify expression inside the bracket, and then will cube it.
Thus, we get:
[tex]\left(\dfrac{x^{-3} y^2}{x^4 y^6}\right)^3 = \left(\dfrac{x^{-3}}{x^4} \times \dfrac{ y^2}{ y^6}\right)^3 = \left(x^{-3} \times x^{-4} \times y^2\times y^{-6}\right)^3 = (x^{-3-4} \times y^{2-6})^3\\\\\left(\dfrac{x^{-3} y^2}{x^4 y^6}\right)^3 = (x^{-7} \times y^{-4})^3 = x^{-7 \times 3} \times y^{-4 \times 3} =x^{-21} \times y^{-12}\\\\\\\left(\dfrac{x^{-3} y^2}{x^4 y^6}\right)^3 = \dfrac{1}{x^{21} y^{12}}[/tex]
Thus, the simplified form of the expression [tex]\left(\dfrac{x^{-3} y^2}{x^4 y^6}\right)^3[/tex] is given by: Option B: [tex]\dfrac{1}{x^{21} y^{12} }[/tex]
Learn more about exponentiation here:
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