Question

7 if g(x) = -2x² + 16, then g(-3) equals (1) -20 (2) -2 (3) 34 (4) 52 8 which equation is always correct? (1) a³ • aˣ = a³ˣ (2) (a⁴)ˣ = a⁴⁺ˣ (3) (ab)ʳ = aʳbʳ (4) aˣ • bʸ = abˣ⁺ʸ

Explanation:

For Question 7:

Step1: Substitute $x=-3$ into $g(x)$

$g(-3) = -2(-3)^2 + 16$

Step2: Calculate the squared term

$(-3)^2 = 9$, so $g(-3) = -2(9) + 16$

Step3: Compute multiplication and addition

$g(-3) = -18 + 16 = -2$

Step1: Check Option (1)

Product rule: $a^m \cdot a^n = a^{m+n}$, so $a^3 \cdot a^x = a^{3+x}
eq a^{3x}$. Incorrect.

Step2: Check Option (2)

Power rule: $(a^m)^n = a^{m \cdot n}$, so $(a^4)^x = a^{4x}
eq a^{4+x}$. Incorrect.

Step3: Check Option (3)

Power of product rule: $(ab)^x = a^x b^x$. Correct.

Step4: Check Option (4)

$a^x \cdot b^y$ cannot be combined into $ab^{x+y}$ (different bases). Incorrect.

Answer:

(2) $-2$

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For Question 8: