what value of n makes the equation true?\n$(2x^{9}y^{n})(4x^{2}y^{10}) = 8x^{11}y^{20}$\n1\n2\n10\n30

what value of n makes the equation true?\n$(2x^{9}y^{n})(4x^{2}y^{10}) = 8x^{11}y^{20}$\n1\n2\n10\n30

what value of n makes the equation true?\n$(2x^{9}y^{n})(4x^{2}y^{10}) = 8x^{11}y^{20}$\n1\n2\n10\n30

Answer

Explanation:

Step1: Multiply the left - hand side terms

Use the rule (a^m\times a^n=a^{m + n}) and ((ab)\times(cd)=(a\times c)(b\times d)). ((2x^{9}y^{n})(4x^{2}y^{10})=(2\times4)x^{9 + 2}y^{n+10}=8x^{11}y^{n + 10})

Step2: Equate the exponents of (y)

Since (8x^{11}y^{n + 10}=8x^{11}y^{20}), then (n+10 = 20). Solve for (n): (n=20 - 10)

Answer:

10