Algebra Examples

${(\frac{7^{3}}{4^{3}})}^{- \frac{1}{3}}$

Step 1

Raise $7$ to the power of $3$ .

${(\frac{343}{4^{3}})}^{- \frac{1}{3}}$

Step 2

Raise $4$ to the power of $3$ .

${(\frac{343}{64})}^{- \frac{1}{3}}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{64}{343})}^{\frac{1}{3}}$

Step 4

Apply the product rule to $\frac{64}{343}$ .

$\frac{64^{\frac{1}{3}}}{343^{\frac{1}{3}}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $64$ as $4^{3}$ .

$\frac{{(4^{3})}^{\frac{1}{3}}}{343^{\frac{1}{3}}}$

Step 5.2

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

$\frac{4^{3 (\frac{1}{3})}}{343^{\frac{1}{3}}}$

Step 5.3

Cancel the common factor of $3$ .

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Step 5.3.1

Cancel the common factor.

$\frac{4^{3 (\frac{1}{3})}}{343^{\frac{1}{3}}}$

Step 5.3.2

Rewrite the expression.

$\frac{4^{1}}{343^{\frac{1}{3}}}$

Step 5.4

Evaluate the exponent.

$\frac{4}{343^{\frac{1}{3}}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $343$ as $7^{3}$ .

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

Step 6.2

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

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

Step 6.3

Cancel the common factor of $3$ .

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Step 6.3.1

Cancel the common factor.

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

Step 6.3.2

Rewrite the expression.

$\frac{4}{7^{1}}$

Step 6.4

Evaluate the exponent.

$\frac{4}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{7}$

Decimal Form:

$0.\overline{571428}$