Question

select the correct answer.

simplify the following expression.

\\(\frac{21m^{42}n^{18}p^{10}}{3m^{21}n^{16}p^5}\\)

• \\(7m^2n^2p\\)
• \\(18m^2n^2p^5\\)
• \\(7m^{21}n^{16}p^5\\)
• \\(18m^{21}n^{16}p^5\\)

Explanation:

⚡ Using what you learned: properties of exponents

Step 1: Divide the coefficients

$$ \frac{21}{3} = 7 $$

Step 2: Simplify the variable \(m\)

Using the quotient rule \(\frac{x^a}{x^b} = x^{a-b}\):

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

Step 3: Simplify the variable \(n\)

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

Step 4: Simplify the variable \(p\)

$$ \frac{p^{10}}{p^9} = p^{10-9} = p^1 $$

Combining all parts gives:

$$ 7m^2n^2p $$

Answer:

\(7m^2n^2p\)