Question

select the correct answer.

which expression is equivalent to the given expression? assume the denominator does not equal zero.
\\(\left(\frac{4m^5n^2}{m^2n}\
ight)^3\\)

\\(64m^9n^3\\)
\\(64m^{13}n^5\\)
\\(12m^6n^4\\)
\\(12m^{21}n^9\\)

Explanation:

⚡ Using what you learned: properties of exponents

Step 1: Simplify inside the parentheses

Simplify the expression inside the parentheses by subtracting the exponents of like bases:

$$ \frac{4m^5n^2}{m^2n} = 4m^{5-2}n^{2-1} = 4m^3n $$

Step 2: Apply the outer exponent

Raise the simplified expression to the power of \(3\):

$$ (4m^3n)^3 = 4^3 \cdot (m^3)^3 \cdot n^3 $$

Step 3: Calculate the final values

Evaluate the coefficient and multiply the exponents:

$$ 4^3 = 64 $$

$$ (m^3)^3 = m^{3 \times 3} = m^9 $$

$$ n^3 = n^3 $$

Combining these gives:

$$ 64m^9n^3 $$

Answer:

\(64m^9n^3\) (the first option)