Use the Laws of logarithms to rewrite the expression $$ \log _{3}\left(x^{13} \sqrt[3]{y^{16}}\right) $$ in a form with no logarithm of a product, quotient or power. After rewriting we have $$ \log _{3}\left(x^{13} \sqrt[3]{y^{16}}\right)=A \log _{3} x+B \log _{3} y $$ with the constant $$ A=\square $$ and the constant $$ B=\square $$

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We start with the expression

$$
\log_{3}\left(x^{13} \sqrt[3]{y^{16}}\right).
$$

Recall that the cube root can be written as an exponent. In particular,

$$
\sqrt[3]{y^{16}} = y^{\frac{16}{3}}.
$$

Thus, the expression becomes

$$
\log_{3}\left(x^{13} y^{\frac{16}{3}}\right).
$$

Next, we apply the logarithm law for products:

$$
\log_b(uv) = \log_b u + \log_b v,
$$

which gives us

$$
\log_{3}\left(x^{13} y^{\frac{16}{3}}\right) = \log_{3}\left(x^{13}\right) + \log_{3}\left(y^{\frac{16}{3}}\right).
$$

Now, we use the logarithm law for powers:

$$
\log_b(u^p) = p \log_b u.
$$

Applying this rule yields

$$
\log_{3}\left(x^{13}\right) = 13 \log_{3} x \quad \text{and} \quad \log_{3}\left(y^{\frac{16}{3}}\right) = \frac{16}{3} \log_{3} y.
$$

Thus, the expression simplifies to

$$
\log_{3}\left(x^{13} \sqrt[3]{y^{16}}\right) = 13 \log_{3} x + \frac{16}{3} \log_{3} y.
$$

Comparing to the form

$$
\log_{3}\left(x^{13} \sqrt[3]{y^{16}}\right) = A \log_{3} x + B \log_{3} y,
$$

we identify the constants as

$$
A = 13 \quad \text{and} \quad B = \frac{16}{3}.
$$
$$ A = 13 $$ and $$ B = \frac{16}{3} $$.

Use the Laws of logarithms to rewrite the expression

in a form with no logarithm of a product, quotient or power.
After rewriting we have

with the constant

and the constant

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Use the Laws of logarithms to rewrite the expression in a form with no logarithm of a product, quotient or power. After rewriting we have with the constant and the constant