Question

simplify the expression to a form in which x is raised to a single integer power.

\\\frac{(x^4)^2 x^{-7}}{x^{-3}}\\

a.) \\(x^{12}\\)

b.) \\(x^{-2}\\)

c.) \\(x^{18}\\)

d.) \\(x^4\\)

Explanation:

Apply the power of a power rule

Using the Exponentiation Rules knowledge point

$$ (x^4)^2 = x^{4 \cdot 2} = x^8 $$

Simplify the numerator

Using the Exponentiation Rules knowledge point

$$ x^8 \cdot x^{-7} = x^{8 + (-7)} = x^1 $$

Divide by the denominator

Using the Exponentiation Rules knowledge point

$$ \frac{x^1}{x^{-3}} = x^{1 - (-3)} = x^{1 + 3} = x^4 $$

Answer:

• a.) \(x^{12}\)
• b.) \(x^{-2}\)
• c.) \(x^{18}\)
• d.) \(x^4\) (Correct answer)