Basic Math Examples

${(\frac{8^{2} \cdot 7^{\frac{1}{3}}}{14^{2}})}^{3}$

Step 1

Evaluate the exponents.

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Step 1.1

Raise $8$ to the power of $2$ .

${(\frac{64 \cdot 7^{\frac{1}{3}}}{14^{2}})}^{3}$

Step 1.2

Raise $14$ to the power of $2$ .

${(\frac{64 \cdot 7^{\frac{1}{3}}}{196})}^{3}$

Step 2

Factor $4$ out of $64 \cdot 7^{\frac{1}{3}}$ .

${(\frac{4 (16 \cdot 7^{\frac{1}{3}})}{196})}^{3}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $4$ out of $196$ .

${(\frac{4 (16 \cdot 7^{\frac{1}{3}})}{4 (49)})}^{3}$

Step 3.2

Cancel the common factor.

${(\frac{4 (16 \cdot 7^{\frac{1}{3}})}{4 \cdot 49})}^{3}$

Step 3.3

Rewrite the expression.

${(\frac{16 \cdot 7^{\frac{1}{3}}}{49})}^{3}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{16 \cdot 7^{\frac{1}{3}}}{49}$ .

$\frac{{(16 \cdot 7^{\frac{1}{3}})}^{3}}{49^{3}}$

Step 4.2

Apply the product rule to $16 \cdot 7^{\frac{1}{3}}$ .

$\frac{16^{3} \cdot {(7^{\frac{1}{3}})}^{3}}{49^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Raise $16$ to the power of $3$ .

$\frac{4096 {(7^{\frac{1}{3}})}^{3}}{49^{3}}$

Step 5.2

Multiply the exponents in ${(7^{\frac{1}{3}})}^{3}$ .

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Step 5.2.1

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

$\frac{4096 \cdot 7^{\frac{1}{3} \cdot 3}}{49^{3}}$

Step 5.2.2

Cancel the common factor of $3$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{4096 \cdot 7^{\frac{1}{3} \cdot 3}}{49^{3}}$

Step 5.2.2.2

Rewrite the expression.

$\frac{4096 \cdot 7^{1}}{49^{3}}$

Step 5.3

Evaluate the exponent.

$\frac{4096 \cdot 7}{49^{3}}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Raise $49$ to the power of $3$ .

$\frac{4096 \cdot 7}{117649}$

Step 6.2

Multiply $4096$ by $7$ .

$\frac{28672}{117649}$

Step 6.3

Cancel the common factor of $28672$ and $117649$ .

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Step 6.3.1

Factor $7$ out of $28672$ .

$\frac{7 (4096)}{117649}$

Step 6.3.2

Cancel the common factors.

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Step 6.3.2.1

Factor $7$ out of $117649$ .

$\frac{7 \cdot 4096}{7 \cdot 16807}$

Step 6.3.2.2

Cancel the common factor.

$\frac{7 \cdot 4096}{7 \cdot 16807}$

Step 6.3.2.3

Rewrite the expression.

$\frac{4096}{16807}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4096}{16807}$

Decimal Form:

$0.24370797 \dots$