Simplify (2 1/3x^(2m-1/2))^2*(3/7x^(1/2))^2

${(2 \frac{1}{3} x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Convert $2 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

${((2 + \frac{1}{3}) x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Add $2$ and $\frac{1}{3}$ .

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

${((2 \cdot \frac{3}{3} + \frac{1}{3}) x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

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

${((\frac{2 \cdot 3}{3} + \frac{1}{3}) x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Combine the numerators over the common denominator.

${(\frac{2 \cdot 3 + 1}{3} x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Simplify the numerator.

Multiply $2$ by $3$ .

${(\frac{6 + 1}{3} x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Add $6$ and $1$ .

${(\frac{7}{3} x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Combine $\frac{7}{3}$ and $x^{2 m - \frac{1}{2}}$ .

${(\frac{7 x^{2 m - \frac{1}{2}}}{3})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Simplify the numerator.

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

${(\frac{7 x^{2 m \cdot \frac{2}{2} - \frac{1}{2}}}{3})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

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

${(\frac{7 x^{\frac{2 m \cdot 2}{2} - \frac{1}{2}}}{3})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Combine the numerators over the common denominator.

${(\frac{7 x^{\frac{2 m \cdot 2 - 1}{2}}}{3})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Multiply $2$ by $2$ .

${(\frac{7 x^{\frac{4 m - 1}{2}}}{3})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

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

Apply the product rule to $\frac{7 x^{\frac{4 m - 1}{2}}}{3}$ .

$\frac{{(7 x^{\frac{4 m - 1}{2}})}^{2}}{3^{2}} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Apply the product rule to $7 x^{\frac{4 m - 1}{2}}$ .

$\frac{7^{2} {(x^{\frac{4 m - 1}{2}})}^{2}}{3^{2}} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Simplify the numerator.

Raise $7$ to the power of $2$ .

$\frac{49 {(x^{\frac{4 m - 1}{2}})}^{2}}{3^{2}} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Multiply the exponents in ${(x^{\frac{4 m - 1}{2}})}^{2}$ .

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

$\frac{49 x^{\frac{4 m - 1}{2} \cdot 2}}{3^{2}} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{49 x^{\frac{4 m - 1}{2} \cdot 2}}{3^{2}} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Rewrite the expression.

$\frac{49 x^{4 m - 1}}{3^{2}} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Combine fractions.

Raise $3$ to the power of $2$ .

$\frac{49 x^{4 m - 1}}{9} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$

Combine $\frac{3}{7}$ and $x^{\frac{1}{2}}$ .

$\frac{49 x^{4 m - 1}}{9} \cdot {(\frac{3 x^{\frac{1}{2}}}{7})}^{2}$

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

Apply the product rule to $\frac{3 x^{\frac{1}{2}}}{7}$ .

$\frac{49 x^{4 m - 1}}{9} \cdot \frac{{(3 x^{\frac{1}{2}})}^{2}}{7^{2}}$

Apply the product rule to $3 x^{\frac{1}{2}}$ .

$\frac{49 x^{4 m - 1}}{9} \cdot \frac{3^{2} {(x^{\frac{1}{2}})}^{2}}{7^{2}}$

Combine.

$\frac{49 x^{4 m - 1} (3^{2} {(x^{\frac{1}{2}})}^{2})}{9 \cdot 7^{2}}$

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{49 x^{4 m - 1} \cdot 9 {(x^{\frac{1}{2}})}^{2}}{9 \cdot 7^{2}}$

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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

$\frac{49 x^{4 m - 1} \cdot 9 x^{\frac{1}{2} \cdot 2}}{9 \cdot 7^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{49 x^{4 m - 1} \cdot 9 x^{\frac{1}{2} \cdot 2}}{9 \cdot 7^{2}}$

Rewrite the expression.

$\frac{49 x^{4 m - 1} \cdot 9 x^{1}}{9 \cdot 7^{2}}$

Simplify.

$\frac{49 x^{4 m - 1} \cdot 9 x}{9 \cdot 7^{2}}$

Combine exponents.

Multiply $9$ by $49$ .

$\frac{441 x^{4 m - 1} x}{9 \cdot 7^{2}}$

Raise $x$ to the power of $1$ .

$\frac{441 (x^{1} x^{4 m - 1})}{9 \cdot 7^{2}}$

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

$\frac{441 x^{1 + 4 m - 1}}{9 \cdot 7^{2}}$

Subtract $1$ from $1$ .

$\frac{441 x^{4 m + 0}}{9 \cdot 7^{2}}$

Add $4 m$ and $0$ .

$\frac{441 x^{4 m}}{9 \cdot 7^{2}}$

Reduce the expression by cancelling the common factors.

Raise $7$ to the power of $2$ .

$\frac{441 x^{4 m}}{9 \cdot 49}$

Multiply $9$ by $49$ .

$\frac{441 x^{4 m}}{441}$

Cancel the common factor of $441$ .

Cancel the common factor.

$\frac{441 x^{4 m}}{441}$

Divide $x^{4 m}$ by $1$ .

$x^{4 m}$

Simplify (2 1/3x^(2m-1/2))^2*(3/7x^(1/2))^2

Related Questions

Support LCMGCF.com by disabling your adblocker.