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$Express the following fraction in simplest form, only using positive exponents. (-2(c^(-5))^(4))/(-5c^(-10)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{-2\left(c^{-5}\right)^{4}}{-5 c^{-10}}$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Express the following fraction in simplest form, only using positive exponents.

\newline

\frac{-2\left(c^{-5}\right)^{4}}{-5 c^{-10}}

\newline

Answer:

Write Expression: Write down the given expression. $\newline$ We have the expression $(-2(c^{-5})^{4})/(-5c^{-10})$ .
Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . So we apply this rule to $(c^{-5})^{4}$ . $\newline$ $(c^{-5})^{4} = c^{-5*4} = c^{-20}$ .
Substitute Simplified Power: Substitute the simplified power of a power into the expression. $\newline$ Now we have $(-2c^{-20})/(-5c^{-10})$ .
Simplify Negative Signs: Simplify the negative signs. $\newline$ Since both the numerator and the denominator have negative signs, they will cancel each other out. $\newline$ So, $(-2c^{-20})/(-5c^{-10})$ becomes $(2c^{-20})/(5c^{-10})$ .
Apply Quotient Rule: Apply the quotient of powers rule. $\newline$ The quotient of powers rule states that $a^{m}/a^{n} = a^{m-n}$ . So we apply this rule to $c^{-20}/c^{-10}$ . $\newline$ $c^{$-20$}/c^{$-10$} = c^{$-20$ - ($-10$)} = c^{$-20$ + $10$} = c^{$-10$}.
Combine Constants and Powers: Combine the constants and the powers of $c$. Now we have $\frac{2}{5} \cdot c^{-10}$.
Express Negative Exponent: Express the negative exponent as a positive exponent.$\newline$To express $c^{-10}$ with a positive exponent, we take the reciprocal of $c$ to the power of $10$.$\newline$$c^{-10} = \frac{1}{c^{10}}$.
Write Final Expression: Write the final simplified expression.$\newline$The final expression is $(\frac{2}{5}) * (\frac{1}{c^{10}})$ which is $\frac{2}{5c^{10}}$.