Question

simplifying with fractional exponents

what expression is equivalent to \\(\frac{27x^{-2}y^6}{3x^5y^2z^0}\\)?

• \\(\frac{9x^7y^4}{z}\\)
• \\(\frac{y^4}{9x^3}\\)
• \\(\frac{9y^4}{x^7}\\)
• \\(\frac{9y^4}{x^7z}\\)

Explanation:

Simplify the numerical coefficients

Using the Algebraic Simplification knowledge point

$$ \frac{27}{3} = 9 $$

Simplify the x terms

Using the Exponent Rules knowledge point

$$ \frac{x^{-2}}{x^5} = x^{-2 - 5} = x^{-7} = \frac{1}{x^7} $$

Simplify the y terms

Using the Exponent Rules knowledge point

$$ \frac{y^6}{y^2} = y^{6 - 2} = y^4 $$

Simplify the z terms

Using the Exponent Rules knowledge point

$$ \frac{1}{z^0} = \frac{1}{1} = 1 $$

Combine all simplified parts

Using the Algebraic Simplification knowledge point

$$ \frac{27x^{-2}y^6}{3x^5y^2z^0} = \frac{9y^4}{x^7} $$

Answer:

• (A) \(\frac{9x^7y^4}{2}\)
• (B) \(\frac{y^4}{9x^3}\)
• (C) \(\frac{9y^4}{x^7}\) (Correct answer)
• (D) \(\frac{9y^4}{x^7z}\)