Question

simplify the following expression.
$\frac{(3c^{2} cdot 2c^{4})^{2}}{c}$
show your work here
hint: to add an exponent ($x^{y}$), type \exponent\ or press \^\
enter your answer

evaluate using the properties of logs.
$7^{log_{7}(6)}$
show your work here

Explanation:

Step1: Multiply coefficients and add exponents

$\frac{(3 \cdot 2 \cdot c^{2+4})^2}{c} = \frac{(6c^6)^2}{c}$

Step2: Apply exponent to the product

$\frac{6^2 \cdot (c^6)^2}{c} = \frac{36c^{12}}{c}$

Step3: Subtract exponents for division

$36c^{12-1} = 36c^{11}$

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Step1: Apply logarithm inverse property

For $a^{\log_a(b)} = b$, here $a=7, b=6$
$7^{\log_7(6)} = 6$

Answer:

1. $36c^{11}$
2. $6$