Algebra Examples

${(\frac{{(2 x^{3})}^{2} {(4 x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1

Simplify the numerator.

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Step 1.1

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

${(\frac{2^{2} {(x^{3})}^{2} {(4 x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.2

Apply the product rule to $4 x^{4}$ .

${(\frac{2^{2} {(x^{3})}^{2} \cdot 4^{2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.3

Combine exponents.

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Step 1.3.1

Rewrite $4$ as $2^{2}$ .

${(\frac{{(2^{2})}^{2} \cdot 2^{2} {(x^{3})}^{2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.3.2

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

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Step 1.3.2.1

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

${(\frac{2^{2 \cdot 2} \cdot 2^{2} {(x^{3})}^{2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.3.2.2

Multiply $2$ by $2$ .

${(\frac{2^{4} \cdot 2^{2} {(x^{3})}^{2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{2^{4 + 2} {(x^{3})}^{2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.3.4

Add $4$ and $2$ .

${(\frac{2^{6} {(x^{3})}^{2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.4

Raise $2$ to the power of $6$ .

${(\frac{64 {(x^{3})}^{2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.5

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

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Step 1.5.1

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

${(\frac{64 x^{3 \cdot 2} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.5.2

Multiply $3$ by $2$ .

${(\frac{64 x^{6} {(x^{4})}^{2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.6

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 1.6.1

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

${(\frac{64 x^{6} x^{4 \cdot 2}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.6.2

Multiply $4$ by $2$ .

${(\frac{64 x^{6} x^{8}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.7

Multiply $x^{6}$ by $x^{8}$ by adding the exponents.

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Step 1.7.1

Move $x^{8}$ .

${(\frac{64 (x^{8} x^{6})}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.7.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{64 x^{8 + 6}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 1.7.3

Add $8$ and $6$ .

${(\frac{64 x^{14}}{8 x^{6}})}^{3} - 312 x^{8}$

Step 2

Cancel the common factor of $64$ and $8$ .

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Step 2.1

Factor $8$ out of $64 x^{14}$ .

${(\frac{8 (8 x^{14})}{8 x^{6}})}^{3} - 312 x^{8}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $8$ out of $8 x^{6}$ .

${(\frac{8 (8 x^{14})}{8 (x^{6})})}^{3} - 312 x^{8}$

Step 2.2.2

Cancel the common factor.

${(\frac{8 (8 x^{14})}{8 x^{6}})}^{3} - 312 x^{8}$

Step 2.2.3

Rewrite the expression.

${(\frac{8 x^{14}}{x^{6}})}^{3} - 312 x^{8}$

Step 3

Cancel the common factor of $x^{14}$ and $x^{6}$ .

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Step 3.1

Factor $x^{6}$ out of $8 x^{14}$ .

${(\frac{x^{6} (8 x^{8})}{x^{6}})}^{3} - 312 x^{8}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

${(\frac{x^{6} (8 x^{8})}{x^{6} \cdot 1})}^{3} - 312 x^{8}$

Step 3.2.2

Cancel the common factor.

${(\frac{x^{6} (8 x^{8})}{x^{6} \cdot 1})}^{3} - 312 x^{8}$

Step 3.2.3

Rewrite the expression.

${(\frac{8 x^{8}}{1})}^{3} - 312 x^{8}$

Step 3.2.4

Divide $8 x^{8}$ by $1$ .

${(8 x^{8})}^{3} - 312 x^{8}$

Step 4

Apply the product rule to $8 x^{8}$ .

$8^{3} {(x^{8})}^{3} - 312 x^{8}$

Step 5

Raise $8$ to the power of $3$ .

$512 {(x^{8})}^{3} - 312 x^{8}$

Step 6

Multiply the exponents in ${(x^{8})}^{3}$ .

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Step 6.1

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

$512 x^{8 \cdot 3} - 312 x^{8}$

Step 6.2

Multiply $8$ by $3$ .

$512 x^{24} - 312 x^{8}$