Question

question 1 of 5
1 point
simplify the expression. your answer should only contain positive exponents.
$2x^{-8}y^{4} \cdot 7x^{6}y^{-2}$
select the correct response:
$14x^{14}y^{6}$
$\frac{14}{x^{2}y^{2}}$
$\frac{14y^{2}}{x^{2}}$
$\frac{y^{2}}{14x^{2}}$

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(2\) and \(7\).
\(2\times7 = 14\)

Step2: Multiply the \(x\)-terms using exponent rule

For the \(x\)-terms \(x^{-8}\) and \(x^{6}\), use the rule \(a^m\cdot a^n=a^{m + n}\).
\(x^{-8}\cdot x^{6}=x^{-8 + 6}=x^{-2}\)

Step3: Multiply the \(y\)-terms using exponent rule

For the \(y\)-terms \(y^{4}\) and \(y^{-2}\), use the rule \(a^m\cdot a^n=a^{m + n}\).
\(y^{4}\cdot y^{-2}=y^{4+( - 2)}=y^{2}\)

Step4: Combine all terms and simplify exponents

Combine the results from Step1, Step2, and Step3: \(14\times x^{-2}\times y^{2}\).
Use the rule \(a^{-n}=\frac{1}{a^{n}}\) to convert \(x^{-2}\) to positive exponent: \(x^{-2}=\frac{1}{x^{2}}\).
So the expression becomes \(\frac{14y^{2}}{x^{2}}\)

Answer:

\(\boldsymbol{\frac{14y^{2}}{x^{2}}}\) (corresponding to the option \(\frac{14y^{2}}{x^{2}}\))