Simplify ((2^6)/(5^3))^(-1/3)

${(\frac{2^{6}}{5^{3}})}^{- \frac{1}{3}}$

Step 1

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

${(\frac{64}{5^{3}})}^{- \frac{1}{3}}$

Step 2

Raise $5$ to the power of $3$ .

${(\frac{64}{125})}^{- \frac{1}{3}}$

Step 3

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

${(\frac{125}{64})}^{\frac{1}{3}}$

Step 4

Apply the product rule to $\frac{125}{64}$ .

$\frac{125^{\frac{1}{3}}}{64^{\frac{1}{3}}}$

Step 5

Simplify the numerator.

Rewrite $125$ as $5^{3}$ .

$\frac{{(5^{3})}^{\frac{1}{3}}}{64^{\frac{1}{3}}}$

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

$\frac{5^{3 (\frac{1}{3})}}{64^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5^{3 (\frac{1}{3})}}{64^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{5^{1}}{64^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{5}{64^{\frac{1}{3}}}$

Step 6

Simplify the denominator.

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

$\frac{5}{{(4^{3})}^{\frac{1}{3}}}$

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

$\frac{5}{4^{3 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5}{4^{3 (\frac{1}{3})}}$

Rewrite the expression.

$\frac{5}{4^{1}}$

Evaluate the exponent.

$\frac{5}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$

Simplify ((2^6)/(5^3))^(-1/3)

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