Algebra Examples

$\frac{2^{- \frac{4}{3}}}{54^{- \frac{4}{3}}}$

Step 1

Move $2^{- \frac{4}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{54^{- \frac{4}{3}} \cdot 2^{\frac{4}{3}}}$

Step 2

Move $54^{- \frac{4}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{54^{\frac{4}{3}}}{2^{\frac{4}{3}}}$

Step 3

Use the power of quotient rule $\frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m}$ .

${(\frac{54}{2})}^{\frac{4}{3}}$

Step 4

Simplify the expression.

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Step 4.1

Divide $54$ by $2$ .

$27^{\frac{4}{3}}$

Step 4.2

Rewrite $27$ as $3^{3}$ .

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

Step 4.3

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

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

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$3^{4}$

Step 6

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

$81$