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$Express the following fraction in simplest form, only using positive exponents. (-3(x)^(-2))/(15x^(5)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{-3(x)^{-2}}{15 x^{5}}$ $\newline$ 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(x)^{-2}}{15 x^{5}}

\newline

Answer:

Write Expression: Write down the given expression. $\newline$ We have the expression $\frac{-3(x)^{-2}}{15x^{5}}$ .
Simplify Coefficients: Simplify the coefficients. $\newline$ Divide the coefficient $-3$ by $15$ to simplify the fraction. $\newline$ $-3 / 15 = -1 / 5$
Apply Exponent Laws: Apply the laws of exponents to simplify the variable part. $\newline$ When dividing powers with the same base, subtract the exponents. $\newline$ $x^{-2} / x^{5} = x^{-2 - 5} = x^{-7}$
Rewrite with Positive Exponents: Rewrite the expression with positive exponents. $\newline$ To express $x^{-7}$ with a positive exponent, write it as $1/x^{7}$ . $\newline$ So, the expression becomes $(-1/5) \times (1/x^{7})$ .
Combine Coefficients and Variables: Combine the coefficients and the variable part. $\newline$ The final simplified expression is $-\frac{1}{5x^{7}}$ .

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