Algebra Examples

$\frac{1}{{(\frac{1}{x^{2}})}^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $\frac{1}{x^{2}}$ .

$\frac{1}{\frac{1^{2}}{{(x^{2})}^{2}}}$

Step 1.2

One to any power is one.

$\frac{1}{\frac{1}{{(x^{2})}^{2}}}$

Step 1.3

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

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Step 1.3.1

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

$\frac{1}{\frac{1}{x^{2 \cdot 2}}}$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{1}{\frac{1}{x^{4}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 x^{4}$

Step 3

Multiply $x^{4}$ by $1$ .

$x^{4}$