Algebra Examples

{(\frac{4 p^{4} r^{4}}{3 p^{2} r^{2}})}^{3}

${(\frac{4 p^{4} r^{4}}{3 p^{2} r^{2}})}^{3}$

Step 1

Cancel the common factor of

p^{4}

$p^{4}$ and

p^{2}

$p^{2}$ .

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Step 1.1

Factor

p^{2}

$p^{2}$ out of

4 p^{4} r^{4}

$4 p^{4} r^{4}$ .

{(\frac{p^{2} (4 p^{2} r^{4})}{3 p^{2} r^{2}})}^{3}

${(\frac{p^{2} (4 p^{2} r^{4})}{3 p^{2} r^{2}})}^{3}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

p^{2}

$p^{2}$ out of

3 p^{2} r^{2}

$3 p^{2} r^{2}$ .

{(\frac{p^{2} (4 p^{2} r^{4})}{p^{2} (3 r^{2})})}^{3}

${(\frac{p^{2} (4 p^{2} r^{4})}{p^{2} (3 r^{2})})}^{3}$

Step 1.2.2

Cancel the common factor.

{(\frac{p^{2} (4 p^{2} r^{4})}{p^{2} (3 r^{2})})}^{3}

${(\frac{p^{2} (4 p^{2} r^{4})}{p^{2} (3 r^{2})})}^{3}$

Step 1.2.3

Rewrite the expression.

{(\frac{4 p^{2} r^{4}}{3 r^{2}})}^{3}

${(\frac{4 p^{2} r^{4}}{3 r^{2}})}^{3}$

{(\frac{4 p^{2} r^{4}}{3 r^{2}})}^{3}

${(\frac{4 p^{2} r^{4}}{3 r^{2}})}^{3}$

{(\frac{4 p^{2} r^{4}}{3 r^{2}})}^{3}

${(\frac{4 p^{2} r^{4}}{3 r^{2}})}^{3}$

Step 2

Cancel the common factor of

r^{4}

$r^{4}$ and

r^{2}

$r^{2}$ .

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Step 2.1

Factor

r^{2}

$r^{2}$ out of

4 p^{2} r^{4}

$4 p^{2} r^{4}$ .

{(\frac{r^{2} (4 p^{2} r^{2})}{3 r^{2}})}^{3}

${(\frac{r^{2} (4 p^{2} r^{2})}{3 r^{2}})}^{3}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

r^{2}

$r^{2}$ out of

3 r^{2}

$3 r^{2}$ .

{(\frac{r^{2} (4 p^{2} r^{2})}{r^{2} \cdot 3})}^{3}

${(\frac{r^{2} (4 p^{2} r^{2})}{r^{2} \cdot 3})}^{3}$

Step 2.2.2

Cancel the common factor.

{(\frac{r^{2} (4 p^{2} r^{2})}{r^{2} \cdot 3})}^{3}

${(\frac{r^{2} (4 p^{2} r^{2})}{r^{2} \cdot 3})}^{3}$

Step 2.2.3

Rewrite the expression.

{(\frac{4 p^{2} r^{2}}{3})}^{3}

${(\frac{4 p^{2} r^{2}}{3})}^{3}$

{(\frac{4 p^{2} r^{2}}{3})}^{3}

${(\frac{4 p^{2} r^{2}}{3})}^{3}$

{(\frac{4 p^{2} r^{2}}{3})}^{3}

${(\frac{4 p^{2} r^{2}}{3})}^{3}$

Step 3

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 3.1

Apply the product rule to

\frac{4 p^{2} r^{2}}{3}

$\frac{4 p^{2} r^{2}}{3}$ .

\frac{{(4 p^{2} r^{2})}^{3}}{3^{3}}

$\frac{{(4 p^{2} r^{2})}^{3}}{3^{3}}$

Step 3.2

Apply the product rule to

4 p^{2} r^{2}

$4 p^{2} r^{2}$ .

\frac{{(4 p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}

$\frac{{(4 p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}$

Step 3.3

Apply the product rule to

4 p^{2}

$4 p^{2}$ .

\frac{4^{3} {(p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}

$\frac{4^{3} {(p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}$

\frac{4^{3} {(p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}

$\frac{4^{3} {(p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}$

Step 4

Simplify the numerator.

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Step 4.1

Raise

4

$4$ to the power of

3

$3$ .

\frac{64 {(p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}

$\frac{64 {(p^{2})}^{3} {(r^{2})}^{3}}{3^{3}}$

Step 4.2

Multiply the exponents in

{(p^{2})}^{3}

${(p^{2})}^{3}$ .

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Step 4.2.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{64 p^{2 \cdot 3} {(r^{2})}^{3}}{3^{3}}

$\frac{64 p^{2 \cdot 3} {(r^{2})}^{3}}{3^{3}}$

Step 4.2.2

Multiply

2

$2$ by

3

$3$ .

\frac{64 p^{6} {(r^{2})}^{3}}{3^{3}}

$\frac{64 p^{6} {(r^{2})}^{3}}{3^{3}}$

\frac{64 p^{6} {(r^{2})}^{3}}{3^{3}}

$\frac{64 p^{6} {(r^{2})}^{3}}{3^{3}}$

Step 4.3

Multiply the exponents in

{(r^{2})}^{3}

${(r^{2})}^{3}$ .

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Step 4.3.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{64 p^{6} r^{2 \cdot 3}}{3^{3}}

$\frac{64 p^{6} r^{2 \cdot 3}}{3^{3}}$

Step 4.3.2

Multiply

2

$2$ by

3

$3$ .

\frac{64 p^{6} r^{6}}{3^{3}}

$\frac{64 p^{6} r^{6}}{3^{3}}$

\frac{64 p^{6} r^{6}}{3^{3}}

$\frac{64 p^{6} r^{6}}{3^{3}}$

\frac{64 p^{6} r^{6}}{3^{3}}

$\frac{64 p^{6} r^{6}}{3^{3}}$

Step 5

Raise

3

$3$ to the power of

3

$3$ .

\frac{64 p^{6} r^{6}}{27}

$\frac{64 p^{6} r^{6}}{27}$