Precalculus Examples

$5^{5 \log ({(\frac{1}{5})}^{x})}$

Step 1

Apply the product rule to $\frac{1}{5}$ .

$5^{5 \log (\frac{1^{x}}{5^{x}})}$

Step 2

One to any power is one.

$5^{5 \log (\frac{1}{5^{x}})}$

Step 3

Simplify $5 \log (\frac{1}{5^{x}})$ by moving $5$ inside the logarithm.

$5^{\log ({(\frac{1}{5^{x}})}^{5})}$

Step 4

Apply the product rule to $\frac{1}{5^{x}}$ .

$5^{\log (\frac{1^{5}}{{(5^{x})}^{5}})}$

Step 5

One to any power is one.

$5^{\log (\frac{1}{{(5^{x})}^{5}})}$

Step 6

Multiply the exponents in ${(5^{x})}^{5}$ .

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Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$5^{\log (\frac{1}{5^{x \cdot 5}})}$

Step 6.2

Move $5$ to the left of $x$ .

$5^{\log (\frac{1}{5^{5 x}})}$