Basic Math Examples

${(4^{5} \cdot 12^{10})}^{- \frac{1}{5}}$

Step 1

Raise $4$ to the power of $5$ .

${(1024 \cdot 12^{10})}^{- \frac{1}{5}}$

Step 2

Raise $12$ to the power of $10$ .

${(1024 \cdot 61917364224)}^{- \frac{1}{5}}$

Step 3

Multiply $1024$ by $61917364224$ .

$63403380965376^{- \frac{1}{5}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{63403380965376^{\frac{1}{5}}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $63403380965376$ as $576^{5}$ .

$\frac{1}{{(576^{5})}^{\frac{1}{5}}}$

Step 5.2

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

$\frac{1}{576^{5 (\frac{1}{5})}}$

Step 5.3

Cancel the common factor of $5$ .

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Step 5.3.1

Cancel the common factor.

$\frac{1}{576^{5 (\frac{1}{5})}}$

Step 5.3.2

Rewrite the expression.

$\frac{1}{576^{1}}$

Step 5.4

Evaluate the exponent.

$\frac{1}{576}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{576}$

Decimal Form:

$0.001736\overline{1}$