Simplify (a^-1b^(-1/3)a^(-4/3)*b^2)^2

${(a^{- 1} \cdot b^{- \frac{1}{3}} \cdot a^{- \frac{4}{3}} \cdot b^{2})}^{2}$

Step 1

Multiply $a^{- 1}$ by $a^{- \frac{4}{3}}$ by adding the exponents.

Move $a^{- \frac{4}{3}}$ .

${(a^{- \frac{4}{3}} a^{- 1} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

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

${(a^{- \frac{4}{3} - 1} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(a^{- \frac{4}{3} - 1 \cdot \frac{3}{3}} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

Combine $- 1$ and $\frac{3}{3}$ .

${(a^{- \frac{4}{3} + \frac{- 1 \cdot 3}{3}} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

Combine the numerators over the common denominator.

${(a^{\frac{- 4 - 1 \cdot 3}{3}} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

${(a^{\frac{- 4 - 3}{3}} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

Subtract $3$ from $- 4$ .

${(a^{\frac{- 7}{3}} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

Move the negative in front of the fraction.

${(a^{- \frac{7}{3}} \cdot b^{- \frac{1}{3}} \cdot b^{2})}^{2}$

Step 2

Multiply $b^{- \frac{1}{3}}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

${(a^{- \frac{7}{3}} \cdot (b^{2} b^{- \frac{1}{3}}))}^{2}$

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

${(a^{- \frac{7}{3}} \cdot b^{2 - \frac{1}{3}})}^{2}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(a^{- \frac{7}{3}} \cdot b^{2 \cdot \frac{3}{3} - \frac{1}{3}})}^{2}$

Combine $2$ and $\frac{3}{3}$ .

${(a^{- \frac{7}{3}} \cdot b^{\frac{2 \cdot 3}{3} - \frac{1}{3}})}^{2}$

Combine the numerators over the common denominator.

${(a^{- \frac{7}{3}} \cdot b^{\frac{2 \cdot 3 - 1}{3}})}^{2}$

Simplify the numerator.

Multiply $2$ by $3$ .

${(a^{- \frac{7}{3}} \cdot b^{\frac{6 - 1}{3}})}^{2}$

Subtract $1$ from $6$ .

${(a^{- \frac{7}{3}} \cdot b^{\frac{5}{3}})}^{2}$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{a^{\frac{7}{3}}} \cdot b^{\frac{5}{3}})}^{2}$

Step 4

Combine $\frac{1}{a^{\frac{7}{3}}}$ and $b^{\frac{5}{3}}$ .

${(\frac{b^{\frac{5}{3}}}{a^{\frac{7}{3}}})}^{2}$

Step 5

Apply basic rules of exponents.

Apply the product rule to $\frac{b^{\frac{5}{3}}}{a^{\frac{7}{3}}}$ .

$\frac{{(b^{\frac{5}{3}})}^{2}}{{(a^{\frac{7}{3}})}^{2}}$

Multiply the exponents in ${(b^{\frac{5}{3}})}^{2}$ .

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

$\frac{b^{\frac{5}{3} \cdot 2}}{{(a^{\frac{7}{3}})}^{2}}$

Multiply $\frac{5}{3} \cdot 2$ .

Combine $\frac{5}{3}$ and $2$ .

$\frac{b^{\frac{5 \cdot 2}{3}}}{{(a^{\frac{7}{3}})}^{2}}$

Multiply $5$ by $2$ .

$\frac{b^{\frac{10}{3}}}{{(a^{\frac{7}{3}})}^{2}}$

Multiply the exponents in ${(a^{\frac{7}{3}})}^{2}$ .

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

$\frac{b^{\frac{10}{3}}}{a^{\frac{7}{3} \cdot 2}}$

Multiply $\frac{7}{3} \cdot 2$ .

Combine $\frac{7}{3}$ and $2$ .

$\frac{b^{\frac{10}{3}}}{a^{\frac{7 \cdot 2}{3}}}$

Multiply $7$ by $2$ .

$\frac{b^{\frac{10}{3}}}{a^{\frac{14}{3}}}$

Simplify (a^-1*b^(-1/3)*a^(-4/3)*b^2)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.

Simplify (a^-1b^(-1/3)a^(-4/3)*b^2)^2