Question

36
$(5x^{2}y^{3})^{2}(4x^{7}y^{4})$ is equivalent to:
a $100x^{11}y^{10}$
b $100x^{11}y^{9}$
c $100x^{28}y^{24}$
d none of the above

Explanation:

Step1: Expand the squared term

Apply power rule: $(a^m b^n)^p = a^{mp}b^{np}$
$(5x^2y^3)^2 = 5^2 x^{2\times2} y^{3\times2} = 25x^4y^6$

Step2: Multiply with the second term

Multiply coefficients, add exponents of like bases: $a^m \times a^n = a^{m+n}$
$25x^4y^6 \times 4x^7y^4 = (25\times4)x^{4+7}y^{6+4} = 100x^{11}y^{10}$

Answer:

A. $100x^{11}y^{10}$