How do you simplify ${(\frac{3 m^{5} r^{3}}{4 p^{8}})}^{4}$ $((3m^5r^3)/(4p^8))^4$ ?

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How do you simplify ${(\frac{3 m^{5} r^{3}}{4 p^{8}})}^{4}$ $((3m^5r^3)/(4p^8))^4$ ?

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Answer 1 · 2017-05-18T01:44:28

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the expression:

$a = a^{1}$ $a = a^color(red)(1)$

${(\frac{3 m^{5} r^{3}}{4 p^{8}})}^{4} \Rightarrow {(\frac{3^{1} m^{5} r^{3}}{4^{1} p^{8}})}^{4}$ $((3m^5r^3)/(4p^8))^4 => ((3^color(red)(1)m^5r^3)/(4^color(red)(1)p^8))^4$

Next, use this rule of equations to complete the simplification:

${(x^{a})}^{b} = x^{a \times b}$ $(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))$

${(\frac{3^{1} m^{5} r^{3}}{4^{1} p^{8}})}^{4} \Rightarrow {(\frac{3^{1} m^{5} r^{3}}{4^{1} p^{8}})}^{4} \Rightarrow \frac{3^{1 \times 4} m^{5 \times 4} r^{3 \times 4}}{4^{1 \times 4} p^{8 \times 4}} \Rightarrow$ $((3^color(red)(1)m^5r^3)/(4^color(red)(1)p^8))^4 => ((3^color(red)(1)m^color(red)(5)r^color(red)(3))/(4^color(red)(1)p^color(red)(8)))^color(blue)(4) => (3^(color(red)(1) xx color(blue)(4))m^(color(red)(5) xx color(blue)(4))r^(color(red)(3) xx color(blue)(4)))/(4^(color(red)(1) xx color(blue)(4))p^(color(red)(8) xx color(blue)(4))) =>$

$\frac{3^{4} m^{20} r^{12}}{4^{4} p^{32}} \Rightarrow \frac{81 m^{20} r^{12}}{256 p^{32}}$ $(3^4m^20r^12)/(4^4p^32) => (81m^20r^12)/(256p^32)$

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How do you simplify ${(\frac{3 m^{5} r^{3}}{4 p^{8}})}^{4}$ $((3m^5r^3)/(4p^8))^4$ ?

1 Answer

Explanation:

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How do you simplify ${(\frac{3 m^{5} r^{3}}{4 p^{8}})}^{4}$ $((3m^5r^3)/(4p^8))^4$ ?