To solve the equation [tex]\( x^{16} y^9 \times ? = x^{26} y^{14} \)[/tex], we need to find the missing term that, when multiplied with [tex]\( x^{16} y^9 \)[/tex], results in the expression [tex]\( x^{26} y^{14} \)[/tex].
Let's denote the missing term as [tex]\( x^a y^b \)[/tex]. Therefore, our equation becomes:
[tex]\[ x^{16} y^9 \times x^a y^b = x^{26} y^{14} \][/tex]
To solve for [tex]\( a \)[/tex] and [tex]\( b \)[/tex], we need to equate the exponents of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] on both sides of the equation.
1. Finding the exponent of [tex]\( x \)[/tex]:
We have:
[tex]\[ 16 + a = 26 \][/tex]
To find [tex]\( a \)[/tex], we solve the equation for [tex]\( a \)[/tex]:
[tex]\[ a = 26 - 16 \][/tex]
So, [tex]\( a = 10 \)[/tex].
2. Finding the exponent of [tex]\( y \)[/tex]:
We have:
[tex]\[ 9 + b = 14 \][/tex]
To find [tex]\( b \)[/tex], we solve the equation for [tex]\( b \)[/tex]:
[tex]\[ b = 14 - 9 \][/tex]
So, [tex]\( b = 5 \)[/tex].
Therefore, the missing term that completes the equation [tex]\( x^{16} y^9 \times ? = x^{26} y^{14} \)[/tex] is [tex]\( x^{10} y^5 \)[/tex].
This gives us the final solution:
[tex]\[ x^{16} y^9 \times x^{10} y^5 = x^{26} y^{14} \][/tex]
Hence, the missing term is [tex]\( x^{10} y^5 \)[/tex].
