Question

question
fully simplify.
16x^5 y^4 (14x^2 y^2)
answer attempt 1 out of 2
submit answer

Explanation:

Step1: Multiply coefficients

Multiply 16 and 14. $16\times14 = 224$

Step2: Multiply \(x\)-terms

Use exponent rule \(a^m\times a^n=a^{m + n}\). For \(x\): \(x^5\times x^2=x^{5 + 2}=x^7\)

Step3: Multiply \(y\)-terms

For \(y\): \(y^4\times y^2=y^{4+2}=y^6\) (Wait, no, wait. Wait the second term is \((14x^{2}y^{2})\)? Wait no, the original expression is \(16x^{5}y^{4}(14x^{2}y^{2})\)? Wait no, looking back, the user's problem: \(16x^{5}y^{4}(14x^{2}y^{2})\)? Wait no, the image shows \(16x^{5}y^{4}(14x^{2}y^{2})\)? Wait no, let me re - check. Wait the expression is \(16x^{5}y^{4}(14x^{2}y^{2})\)? Wait, no, maybe I misread. Wait the problem is \(16x^{5}y^{4}(14x^{2}y^{2})\)? Wait, no, let's do it correctly.

Wait, actually, the correct way: when multiplying monomials, we multiply the coefficients and add the exponents of like bases.

Coefficients: \(16\times14 = 224\)

For \(x\): \(x^{5}\times x^{2}=x^{5 + 2}=x^{7}\)

For \(y\): \(y^{4}\times y^{2}=y^{4+2}=y^{6}\)

Wait, but wait, maybe the original problem was \(16x^{5}y^{4}(14x^{2}y^{2})\)? Wait, no, let's check again. Wait the user's problem: "Fully simplify. \(16x^{5}y^{4}(14x^{2}y^{2})\)"? Wait, no, maybe there was a typo, but assuming that, then:

So combining all together: \(224x^{7}y^{6}\)

Wait, but wait, maybe I made a mistake. Wait, let's recalculate the coefficient: \(16\times14\). \(10\times14 = 140\), \(6\times14 = 84\), \(140+84 = 224\). Correct. For \(x\): \(x^{5}\times x^{2}=x^{7}\), for \(y\): \(y^{4}\times y^{2}=y^{6}\). So the simplified form is \(224x^{7}y^{6}\)

Wait, but wait, maybe the original problem was \(16x^{5}y^{4}(14x^{2}y^{2})\)? Yes, that seems to be the case. So the steps are:

1. Multiply the numerical coefficients: \(16\times14 = 224\)
2. Multiply the \(x\) - variables using the product rule of exponents (\(a^{m}\cdot a^{n}=a^{m + n}\)): \(x^{5}\cdot x^{2}=x^{5 + 2}=x^{7}\)
3. Multiply the \(y\) - variables using the product rule of exponents: \(y^{4}\cdot y^{2}=y^{4+2}=y^{6}\)

Then, the simplified expression is \(224x^{7}y^{6}\)

Answer:

\(224x^{7}y^{6}\)