Simplify. ((20m^(9)n^(-5)p^(7))/(15m^(-4)n^(-2)p^(-7)))^(-1) Write your answer using only positive exponents.

Rewrite with positive exponents: Rewrite the expression with positive exponents by taking the reciprocal of the fraction. ((20m^(9)n^(-5)p^(7))/(15m^(-4)n^(-2)p^(-7)))^(-1) = (15m^(-4)n^(-2)p^(-7))/(20m^(9)n^(-5)p^(7))Combine exponents using properties: Simplify the expression by combining the exponents using the properties of exponents. (15/20) * (m^(-4-9)) * (n^(-2+5)) * (p^(-7-7))Simplify coefficients and exponents: Simplify the coefficients and the exponents. (15/20) simplifies to (3/4) since both 15 and 20 are divisible by 5. m^(-4-9) simplifies to m^(-13). n^(-2+5) simplifies to n^(3). p^(-7-7) simplifies to p^(-14). So, the expression becomes (3/4)m^(-13)n^(3)p^(-14).Rewrite with positive exponents: Rewrite the expression with only positive exponents. (3/4)m^(-13)n^(3)p^(-14) = (3/4)(1/m^(13))(n^(3))(1/p^(14))Combine terms with positive exponents: Combine the terms with positive exponents. (3/4)(n^(3))/(m^(13)p^(14))

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Math Problems

Grade 8

Divide numbers written in scientific notation

Full solution

Q. Simplify.

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\left(\frac{20 m^{9} n^{-5} p^{7}}{15 m^{-4} n^{-2} p^{-7}}\right)^{-1}

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Write your answer using only positive exponents.

Rewrite with positive exponents: Rewrite the expression with positive exponents by taking the reciprocal of the fraction. $\newline$ $\left(\frac{20m^{9}n^{-5}p^{7}}{15m^{-4}n^{-2}p^{-7}}\right)^{-1} = \frac{15m^{-4}n^{-2}p^{-7}}{20m^{9}n^{-5}p^{7}}$
Combine exponents using properties: Simplify the expression by combining the exponents using the properties of exponents. $(\frac{15}{20}) \cdot (m^{(-4-9)}) \cdot (n^{(-2+5)}) \cdot (p^{(-7-7)})$
Simplify coefficients and exponents: Simplify the coefficients and the exponents. $\newline$ $(\frac{15}{20})$ simplifies to $(\frac{3}{4})$ since both $15$ and $20$ are divisible by $5$ . $\newline$ $m^{(-4-9)}$ simplifies to $m^{(-13)}$ . $\newline$ $n^{(-2+5)}$ simplifies to $n^{3}$ . $\newline$ $p^{(-7-7)}$ simplifies to $(\frac{3}{4})$ $0$ . $\newline$ So, the expression becomes $(\frac{3}{4})$ $1$ .
Rewrite with positive exponents: Rewrite the expression with only positive exponents. $\newline$ $(\frac{3}{4})m^{-13}n^{3}p^{-14} = (\frac{3}{4})(\frac{1}{m^{13}})(n^{3})(\frac{1}{p^{14}})$
Combine terms with positive exponents: Combine the terms with positive exponents. $\newline$ $(\frac{3}{4})\frac{n^{3}}{m^{13}p^{14}}$