Question

Simplify 1/6^3 divided by 1/36

Answer 1

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:

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

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 divide 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

Answer 2

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!