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$Express the following fraction in simplest form, only using positive exponents. (3y^(10))/(-3(w)^(5)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{3 y^{10}}{-3(w)^{5}}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

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

\newline

\frac{3 y^{10}}{-3(w)^{5}}

\newline

Answer:

Identify negative base: Identify the negative base in the denominator and rewrite the fraction. $\newline$ The fraction given is $(3y^{10})/(-3(w)^{5})$ . We notice that the base $-3$ in the denominator can be rewritten as $-1$ times $3$ to separate the negative sign from the base.
Cancel common factors: Cancel out common factors in the numerator and the denominator. $\newline$ We have $3$ in the numerator and $3$ in the denominator, which can be canceled out because they are common factors. $\newline$ $\frac{3y^{10}}{3(-1)(w)^{5}} = \frac{y^{10}}{(-1)(w)^{5}}$
Remove negative sign: Simplify the expression by removing the negative sign. Since we are only dealing with the magnitude and want positive exponents, we can remove the negative sign from the denominator as it does not affect the exponent. $y^{10}/w^{5}$
Write final expression: Write the final simplified expression. $\newline$ The final simplified expression with positive exponents is $\frac{y^{10}}{w^{5}}$ .

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