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Sagot :
Answer:
1/6
Step-by-step explanation:
To simplify the expression:
1. Change the divisor into it's reciprocal
2. Change the sign into a multiplication sign.
3. Evaluate the product of those fractions.
4. Simplify the fraction. (If possible)
Given expression:
[tex]\dfrac{1}{6^3 } \div \dfrac{1}{36}[/tex]
According to step 1, we need to convert the divisor of the expression into it's reciprocal.
[tex]\dfrac{1}{6^3 } \div \dfrac{36}{1}[/tex]
According to step 2, we need to change the division sign (÷) into a multiplication sign (×).
[tex]\implies \dfrac{1}{6^3 } \times \dfrac{36}{1}[/tex]
According to step 3, we need to determine the product of these fractions. This can be done by evaluating the exponent.
[tex]\implies \dfrac{1}{(6)(6)(6) } \times \dfrac{36}{1}[/tex]
[tex]\implies \dfrac{1}{216 } \times \dfrac{36}{1}[/tex]
Multiply the fractions as needed. [a/b × c/d = (a × c)/(b × d) = (ac)/(bd):
[tex]\implies \dfrac{36}{216 }[/tex]
According to step 4, (If possible), Simplify the product of 1/216 and 36. In this case, the product of 1/216 and 36 is 36/216. Since both are divisible by 6, we can divide the numerator and the denominator by 6 to simplify the fraction.
[tex]\implies \dfrac{36 \div 6}{216 \div 6 }[/tex]
[tex]\implies \dfrac{1}{6 }[/tex]
Therefore, the quotient of 1/6^3 and 1/36 is 1/6.
Learn more about this topic: https://brainly.com/question/22322495
Answer:
[tex]\large\textsf{$\dfrac{1}{6}$}[/tex]
Step-by-step explanation:
[tex]\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{36}$} \implies \normalsize \textsf{Convert 36 into a base with an exponent}[/tex]
[tex]\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{6^2}$} \implies \normalsize \textsf{Cross multiply}[/tex]
[tex]\large\textsf{$\dfrac{1 \cdot 6^2}{1 \cdot 6^3}$} \implies \normalsize \textsf{Multiply}[/tex]
[tex]\large\textsf{$\dfrac{6^2}{6^3}$}\implies \normalsize \textsf{Simplify using the Quotient of Powers Property: \normalsize\textsf{$\dfrac{x^m}{x^n} = x^{m-n}$}}[/tex]
[tex]\large\textsf6^{2-3}[/tex]
[tex]\large\textsf6^{-1} \implies \normalsize \textsf{Simplify using the Negative Exponent Property: \normalsize\textsf {${x^{-m}} = \dfrac{1}{x^m}$}}[/tex]
[tex]\large\textsf{$\dfrac{1}{6^1}$} \implies \normalsize \textsf{Simplify}[/tex]
[tex]\large\textsf{$\dfrac{1}{6}$} \implies \normalsize \textsf{Final answer}[/tex]
Hope this helps!
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