Question

1 multiple choice 5 points the expression $3a^{2}b^{3} \cdot 5a^{3}b^{2} \cdot 4b^{2}$ is equal to: $12a^{5}b^{7}$ $12a^{6}b^{12}$ $60a^{5}b^{7}$ $60a^{6}b^{12}$ $60a^{6}b^{7}$ 2 multiple choice 5 points the expression $(5xy^{3})(2x^{2}y)$ $7x^{2}y4$ $7x^{3}y^{3}$ $10x^{2}y^{3}$ $10x^{2}y^{4}$ $10x^{3}y^{4}$ 3 multiple choice 5 points the expression $(x^{8})^{16}$ is equivalent to: $x^{-8}$ $x^{2}$ $x^{8}$ $x^{24}$ $x^{128}$

Explanation:

Step1: Multiply coefficients

$3 \times 5 \times 4 = 60$

Step2: Combine $a$-terms (add exponents)

$a^2 \times a^3 = a^{2+3} = a^5$

Step3: Combine $b$-terms (add exponents)

$b^3 \times b^2 \times b^2 = b^{3+2+2} = b^7$

Step4: Multiply coefficients (Q2)

$5 \times 2 = 10$

Step5: Combine $x$-terms (add exponents)

$x^1 \times x^2 = x^{1+2} = x^3$

Step6: Combine $y$-terms (add exponents)

$y^3 \times y^1 = y^{3+1} = y^4$

Step7: Apply power rule (Q3)

$(x^8)^{16} = x^{8 \times 16} = x^{128}$

Answer:

1. $60a^5b^7$
2. $10x^3y^4$
3. $x^{128}$