Question

select the equivalent expression.
\\(\frac{x^2 \cdot x^3}{x^{-2}}\\)
answer
\\(\frac{1}{x^3}\\) \\(x^7\\) \\(\frac{1}{x^7}\\) \\(x^3\\)

Explanation:

Step1: Simplify numerator (product of exponents)

When multiplying exponents with the same base, we add the exponents. So \( x^2 \cdot x^3 = x^{2 + 3} = x^5 \).

Step2: Simplify the fraction (dividing exponents)

When dividing exponents with the same base, we subtract the exponents. So \( \frac{x^5}{x^{-2}} = x^{5 - (-2)} \).

Step3: Calculate the exponent

\( 5 - (-2) = 5 + 2 = 7 \), so the expression simplifies to \( x^7 \).

Answer:

\( x^7 \) (the option with \( x^7 \))