College Algebra · Question of the Day

College Algebra Question of the Day

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Saturday, October 17, 2026

Given that $a = 2^x$ and $b = 3^x$ , express $6^x + 6^{x+1}$ in terms of $a$ and $b$ .

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Question of the Day

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Given that $a = 2^x$ and $b = 3^x$ , express $6^x + 6^{x+1}$ in terms of $a$ and $b$ .

$ab + 6ab$
$7ab$ (correct answer)
$ab + ab^2$
$a + b + 6ab$

Explanation: First, note that $6^x = (2 \cdot 3)^x = 2^x \cdot 3^x = ab$ . Also, $6^{x+1} = 6^x \cdot 6^1 = 6 \cdot 6^x = 6ab$ . Therefore: $6^x + 6^{x+1} = ab + 6ab = 7ab$ . Choice A shows the intermediate step but doesn't combine like terms. Choice C incorrectly treats the exponent $x+1$ as affecting only the base 3. Choice D incorrectly adds separate $a$ and $b$ terms that don't correspond to the original expression.