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Alexus [3.1K]
2 years ago
12

Simplify 1/6^3 divided by 1/36

Mathematics
2 answers:
VladimirAG [237]2 years ago
5 0

Answer:

1/6

Step-by-step explanation:

To simplify the expression:

      1. <u>Change</u> the divisor into it's reciprocal

     2. <u>Change</u> the sign into a multiplication sign.

     3. <u>Evaluate</u> the product of those fractions.

     4. <u>Simplify</u> the fraction. (If possible)

Given expression:

\dfrac{1}{6^3 } \div \dfrac{1}{36}

According to step 1, we need to convert the divisor of the expression into it's reciprocal.

\dfrac{1}{6^3 } \div \dfrac{36}{1}

According to step 2, we need to change the division sign (÷) into a multiplication sign (×).

\implies \dfrac{1}{6^3 } \times \dfrac{36}{1}

According to step 3, we need to determine the product of these fractions. This can be done by evaluating the exponent.

\implies \dfrac{1}{(6)(6)(6) } \times \dfrac{36}{1}

\implies \dfrac{1}{216 } \times \dfrac{36}{1}

Multiply the fractions as needed. [a/b × c/d = (a × c)/(b × d) = (ac)/(bd):

\implies \dfrac{36}{216 }

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 <u>divide</u> the numerator and the denominator by 6 to simplify the fraction.

\implies \dfrac{36 \div 6}{216 \div 6 }

\implies \dfrac{1}{6 }

Therefore, the quotient of 1/6^3 and 1/36 is 1/6.

Learn more about this topic: brainly.com/question/22322495

leonid [27]2 years ago
5 0

Answer:

\large\textsf{$\dfrac{1}{6}$}

Step-by-step explanation:

\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{36}$} \implies \normalsize \textsf{Convert 36 into a base with an exponent}

\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{6^2}$} \implies \normalsize \textsf{Cross multiply}

\large\textsf{$\dfrac{1 \cdot 6^2}{1 \cdot 6^3}$} \implies \normalsize \textsf{Multiply}

\large\textsf{$\dfrac{6^2}{6^3}$}\implies \normalsize \textsf{Simplify using the Quotient of Powers Property: \normalsize\textsf{$\dfrac{x^m}{x^n} = x^{m-n}$}}

\large\textsf6^{2-3}

\large\textsf6^{-1} \implies \normalsize \textsf{Simplify using the Negative Exponent Property: \normalsize\textsf {${x^{-m}} = \dfrac{1}{x^m}$}}

\large\textsf{$\dfrac{1}{6^1}$} \implies \normalsize \textsf{Simplify}

\large\textsf{$\dfrac{1}{6}$} \implies \normalsize \textsf{Final answer}

Hope this helps!

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