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$Evaluate the expression shown below and write your answer as a fraction in simplest form. -(8)/(9)-(2)/(63) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $-\frac{8}{9}-\frac{2}{63}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.

\newline

-\frac{8}{9}-\frac{2}{63}

\newline

Answer:

Find Common Denominator: Identify a common denominator for the fractions. $\newline$ The fractions $-\frac{8}{9}$ and $-\frac{2}{63}$ have different denominators. To combine them, we need to find a common denominator. The least common multiple (LCM) of $9$ and $63$ is $63$ .
Convert Fractions: Convert the fractions to have the common denominator. $\newline$ The first fraction $-\frac{8}{9}$ needs to be converted to have a denominator of $63$ . We do this by multiplying both the numerator and the denominator by $7$ (since $63$ is $7$ times $9$ ). $\newline$ So, $-\frac{8}{9}$ becomes $-\frac{8\times 7}{9\times 7} = -\frac{56}{63}$ . $\newline$ The second fraction $-\frac{2}{63}$ already has the common denominator, so it remains unchanged.
Combine Fractions: Combine the fractions. $\newline$ Now that both fractions have the same denominator, we can combine them by adding their numerators together. $\newline$ So, $-\frac{56}{63}$ - $\frac{2}{63}$ = $\frac{-56 - 2}{63}$ = $-\frac{58}{63}$ .
Simplify Result: Simplify the fraction, if possible. $\newline$ The fraction $-\frac{58}{63}$ cannot be simplified further because $58$ and $63$ do not have any common factors other than $1$ .

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