Basic Math Examples

$\log ({(\frac{k^{2} m^{3}}{p^{3} t})}^{- 2})$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

$\log ({(\frac{p^{3} t}{k^{2} m^{3}})}^{2})$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{p^{3} t}{k^{2} m^{3}}$ .

$\log (\frac{{(p^{3} t)}^{2}}{{(k^{2} m^{3})}^{2}})$

Step 2.2

Apply the product rule to $p^{3} t$ .

$\log (\frac{{(p^{3})}^{2} t^{2}}{{(k^{2} m^{3})}^{2}})$

Step 2.3

Apply the product rule to $k^{2} m^{3}$ .

$\log (\frac{{(p^{3})}^{2} t^{2}}{{(k^{2})}^{2} {(m^{3})}^{2}})$

Step 3

Multiply the exponents in ${(p^{3})}^{2}$ .

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Step 3.1

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

$\log (\frac{p^{3 \cdot 2} t^{2}}{{(k^{2})}^{2} {(m^{3})}^{2}})$

Step 3.2

Multiply $3$ by $2$ .

$\log (\frac{p^{6} t^{2}}{{(k^{2})}^{2} {(m^{3})}^{2}})$

Step 4

Simplify the denominator.

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Step 4.1

Multiply the exponents in ${(k^{2})}^{2}$ .

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Step 4.1.1

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

$\log (\frac{p^{6} t^{2}}{k^{2 \cdot 2} {(m^{3})}^{2}})$

Step 4.1.2

Multiply $2$ by $2$ .

$\log (\frac{p^{6} t^{2}}{k^{4} {(m^{3})}^{2}})$

Step 4.2

Multiply the exponents in ${(m^{3})}^{2}$ .

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Step 4.2.1

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

$\log (\frac{p^{6} t^{2}}{k^{4} m^{3 \cdot 2}})$

Step 4.2.2

Multiply $3$ by $2$ .

$\log (\frac{p^{6} t^{2}}{k^{4} m^{6}})$