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Simplify: 3x² sqrt(6x) + 2

March 21, 2026Mathematics

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Answer

24^x

5 steps

Start with the given expression.
$\frac{2^{6x-2} \cdot 3^x}{2^{3x-2}}$
Apply the quotient of powers rule
$\frac{a^m}{a^n} = a^{m-n}$ .
$\frac{2^{6x-2}}{2^{3x-2}} \cdot 3^x = 2^{(6x-2)-(3x-2)} \cdot 3^x$
Simplify the exponent.
$(6x-2) - (3x-2) = 6x - 2 - 3x + 2 = 3x$ $2^{3x} \cdot 3^x$
Rewrite using power of a power rule.
$2^{3x} = (2^3)^x = 8^x$ $8^x \cdot 3^x$
Apply the product of powers rule
$a^m \cdot b^m = (a \cdot b)^m$ .
$(8 \cdot 3)^x = 24^x$
** 24^x **

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