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

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

\newline

Answer:

Write Expression: Write down the given expression. $\newline$ We have the expression $(-5p^{-5})/((3p^{2})^{5})$ .
Simplify Denominator: Simplify the denominator. $\newline$ The denominator is $(3p^{2})^{5}$ . According to the power of a power rule, we multiply the exponents. $\newline$ $(3p^{2})^{5} = 3^{5} \times (p^{2})^{5} = 3^{5} \times p^{2\times5} = 3^{5} \times p^{10}$ .
Rewrite Expression: Rewrite the expression with the simplified denominator. $\newline$ Now the expression is $(-5p^{-5})/(3^5 \cdot p^{10})$ .
Deal with Negative Exponent: Simplify the expression by dealing with the negative exponent in the numerator. A negative exponent means that the base is on the wrong side of the fraction line, so we move it to the denominator to make the exponent positive. $\frac{-5}{3^5 \cdot p^{10}} \cdot p^5$ .
Calculate Value: Calculate the value of $3^5$ . $\newline$ $3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$ .
Combine Terms: Combine the terms in the denominator. $\newline$ Now we have $(-5)/(243 \cdot p^{10}) \cdot p^{5}$ .
Combine $p$ Terms: Simplify the expression by combining the $p$ terms. $\newline$ We subtract the exponents of $p$ because we are dividing powers with the same base. $\newline$ $(-5)/(243 \cdot p^{10-5}) = (-5)/(243 \cdot p^5)$ .
Write Final Expression: Write the final simplified expression. $\newline$ The final simplified expression is $(-5)/(243 \cdot p^5)$ .

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