B1. Solve the exponential equation $16 \cdot 16 \sqrt{4^{5 x}}=\sqrt[4]{4^{3 x+10}} \cdot \sqrt[3]{4^{5 x+1}}$.
B1. We rearrange the equation so that both sides are written in the form of a power of $4^{4+\frac{5 x}{2}}=4^{\frac{3 x+10}{4}} \cdot 4^{\frac{5 x+1}{3}}$. On the right side, we perform the multiplication of the powers and get

$4^{4+\frac{5 x}{2}}=4^{\frac{29 x+34}{12}}$. We apply the rule for solving exponential equations and equate the exponents $4+\frac{5 x}{2}=\frac{29 x+34}{12}$. We eliminate the fraction $48+30 x=29 x+34$, rearrange the resulting linear equation, and obtain the solution $x=-14$.

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Multiplication of powers with the same base $4^{\frac{3 x+10}{4}} \cdot 4^{\frac{5 x+1}{3}}=4^{\frac{29 x+34}{12}} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots 1$ point

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Solving the linear equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 point

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