Question

find the gcf of the given list
x^{17}y^{4}, x^{2}y^{4}, x^{6}y^{8}
the gcf of x^{17}y^{4}, x^{2}y^{4}, and x^{6}y^{8} is
(simplify your answer.)

Explanation:

Step1: Find GCF of x-terms

For \( x^{17} \), \( x^2 \), \( x^6 \), the exponents are 17, 2, 6. The smallest exponent is 2, so GCF for x is \( x^2 \).

Step2: Find GCF of y-terms

For \( y^4 \), \( y^4 \), \( y^8 \), the exponents are 4, 4, 8. The smallest exponent is 4, so GCF for y is \( y^4 \).

Step3: Combine GCFs

Multiply the GCF of x and GCF of y: \( x^2 \cdot y^4 = x^2y^4 \).

Answer:

\( x^2y^4 \)