5) $$ 2 x^{2} y^{5} \cdot 9 x^{4} y^{2} $$

Question

UpStudy AI · Accepted Answer

Given the expression

$$
2 x^{2} y^{5} \cdot 9 x^{4} y^{2},
$$

we start by multiplying the numerical coefficients:

$$
2 \cdot 9 = 18.
$$

Next, we apply the law of exponents for the $$ x $$ terms. When multiplying like bases, we add the exponents:

$$
x^{2} \cdot x^{4} = x^{2+4} = x^{6}.
$$

Similarly, for the $$ y $$ terms:

$$
y^{5} \cdot y^{2} = y^{5+2} = y^{7}.
$$

Combining all the results together, we have:

$$
18 x^{6} y^{7}.
$$
The simplified expression is $$ 18x^{6}y^{7} $$.

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