Question

simplify:
\\((2x^3)^3\\)

• \\(2x^6\\)
• \\(2x^9\\)
• \\(8x^6\\)
• \\(8x^9\\)

question 4

simplify:
\\((3x^5y^{-7})^2\\)

• \\(\frac{9x^{10}}{y^{14}}\\)
• \\(\frac{6x^{10}}{y^{14}}\\)
• \\(\frac{1}{9x^{10}y^{14}}\\)
• \\(9\frac{x^7}{y^9}\\)

Explanation:

Distribute the outer exponent to each factor in the first expression

$$ (2x^3)^3 = 2^3 \cdot (x^3)^3 $$

Simplify the numerical base and apply the power of a power rule

$$ 2^3 = 8 $$

$$ (x^3)^3 = x^{3 \cdot 3} = x^9 $$

$$ (2x^3)^3 = 8x^9 $$

Distribute the outer exponent and apply negative exponent rules to the second expression

$$ (3x^5y^{-7})^2 = 3^2 \cdot (x^5)^2 \cdot (y^{-7})^2 $$

$$ 3^2 = 9 $$

$$ (x^5)^2 = x^{5 \cdot 2} = x^{10} $$

$$ (y^{-7})^2 = y^{-7 \cdot 2} = y^{-14} = \frac{1}{y^{14}} $$

$$ (3x^5y^{-7})^2 = \frac{9x^{10}}{y^{14}} $$

Answer:

Question 1

• (A) \(2x^6\)
• (B) \(2x^9\)
• (C) \(8x^6\)
• (D) \(8x^9\) (Correct answer)

Question 2

• (A) \(\frac{9x^{10}}{y^{14}}\) (Correct answer)
• (B) \(\frac{6x^{10}}{y^{14}}\)
• (C) \(\frac{1}{9x^{10}y^{14}}\)
• (D) \(9\frac{x^7}{y^9}\)