Algebra Examples

${(\frac{2}{3 r^{2} t^{3} z^{6}})}^{2}$

Step 1

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

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Step 1.1

Apply the product rule to $\frac{2}{3 r^{2} t^{3} z^{6}}$ .

$\frac{2^{2}}{{(3 r^{2} t^{3} z^{6})}^{2}}$

Step 1.2

Apply the product rule to $3 r^{2} t^{3} z^{6}$ .

$\frac{2^{2}}{{(3 r^{2} t^{3})}^{2} {(z^{6})}^{2}}$

Step 1.3

Apply the product rule to $3 r^{2} t^{3}$ .

$\frac{2^{2}}{{(3 r^{2})}^{2} {(t^{3})}^{2} {(z^{6})}^{2}}$

Step 1.4

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

$\frac{2^{2}}{3^{2} {(r^{2})}^{2} {(t^{3})}^{2} {(z^{6})}^{2}}$

Step 2

Raise $2$ to the power of $2$ .

$\frac{4}{3^{2} {(r^{2})}^{2} {(t^{3})}^{2} {(z^{6})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $3$ to the power of $2$ .

$\frac{4}{9 {(r^{2})}^{2} {(t^{3})}^{2} {(z^{6})}^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{4}{9 r^{2 \cdot 2} {(t^{3})}^{2} {(z^{6})}^{2}}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{4}{9 r^{4} {(t^{3})}^{2} {(z^{6})}^{2}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{4}{9 r^{4} t^{3 \cdot 2} {(z^{6})}^{2}}$

Step 3.3.2

Multiply $3$ by $2$ .

$\frac{4}{9 r^{4} t^{6} {(z^{6})}^{2}}$

Step 3.4

Multiply the exponents in ${(z^{6})}^{2}$ .

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Step 3.4.1

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

$\frac{4}{9 r^{4} t^{6} z^{6 \cdot 2}}$

Step 3.4.2

Multiply $6$ by $2$ .

$\frac{4}{9 r^{4} t^{6} z^{12}}$