Question

progress xxx1. evaluate$(x^{2}y^{3})(x^{5}y^{7})$2. evaluate$(x^{3})(y^{3})(xy^{4})$3. evaluate$(7x^{3}y^{9})(x^{7})(y^{8})$4. evaluate$(2xy^{2})(y^{3})(3x^{8})$answersa: $x^{3}y^{7}$b: $x^{10}y^{21}$c: $7x^{21}y^{72}$d: $6x^{8}y^{6}$e: $7x^{21}y^{17}$f: $6x^{8}y^{5}$g: $x^{7}y^{21}$h: $x^{10}y^{10}$i: $x^{4}y^{12}$j: $7x^{9}y^{5}$k: $6x^{9}y^{6}$l: $6x^{9}y^{5}$m: $7x^{10}y^{17}$n: $x^{4}y^{7}$o: $x^{7}y^{10}$

Explanation:

Step1: Group like variables

$(x^2y^3)(x^5y^7) = (x^2 \cdot x^5)(y^3 \cdot y^7)$

Step2: Apply exponent rule $a^m \cdot a^n=a^{m+n}$

$x^{2+5}y^{3+7} = x^7y^{10}$

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Step1: Group like variables

$(x^3)(y^3)(xy^4) = (x^3 \cdot x)(y^3 \cdot y^4)$

Step2: Apply exponent rule $a^m \cdot a^n=a^{m+n}$

$x^{3+1}y^{3+4} = x^4y^7$

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Step1: Group like variables

$(7x^3y^9)(x^7)(y^8) = 7(x^3 \cdot x^7)(y^9 \cdot y^8)$

Step2: Apply exponent rule $a^m \cdot a^n=a^{m+n}$

$7x^{3+7}y^{9+8} = 7x^{10}y^{17}$

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Step1: Group like variables

$(2xy^2)(y^3)(3x^8) = (2 \cdot 3)(x \cdot x^8)(y^2 \cdot y^3)$

Step2: Multiply coefficients, apply exponent rule

$6x^{1+8}y^{2+3} = 6x^9y^5$

Answer:

1. $\boldsymbol{O: x^7y^{10}}$
2. $\boldsymbol{N: x^4y^7}$
3. $\boldsymbol{M: 7x^{10}y^{17}}$
4. $\boldsymbol{L: 6x^9y^5}$