Question

Describe how you would simplify the given expression. (20x^5y^2/5x^-3y^7)-3​

Answer 1

`\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\`

`\bf \left( \cfrac{20x^5y^2}{5x^(-3)y^7} \right)^(-3)\implies \left( \cfrac{5x^(-3)y^7}{20x^5y^2} \right)^3\implies \left( \cfrac{5^3x^(-3\cdot 3)y^(7\cdot 3)}{20^3x^(5\cdot 3)y^(2\cdot 3)} \right)\implies \cfrac{5^3}{20^3}\cdot \cfrac{x^(-9)y^(21)}{x^(15)y^6} \\\\\\ \cfrac{1}{64}\cdot \cfrac{y^(21)\cdot y^(-6)}{x^(15)\cdot x^9}\implies \cfrac{1}{64}\cdot \cfrac{y^(21-6)}{x^(15+9)}\implies \cfrac{y^(15)}{64x^(24)}`

Answer 2

Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.

Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.

Explanation: