Algebra Examples

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

Step 1

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

${(3 x^{2} \frac{1}{y^{3}})}^{2} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 2

Multiply $3 x^{2} \frac{1}{y^{3}}$ .

Tap for more steps...

Step 2.1

Combine $3$ and $\frac{1}{y^{3}}$ .

${(x^{2} \frac{3}{y^{3}})}^{2} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 2.2

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

${(\frac{x^{2} \cdot 3}{y^{3}})}^{2} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 3

Move $3$ to the left of $x^{2}$ .

${(\frac{3 \cdot x^{2}}{y^{3}})}^{2} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 4

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

Tap for more steps...

Step 4.1

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

$\frac{{(3 x^{2})}^{2}}{{(y^{3})}^{2}} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 4.2

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

$\frac{3^{2} {(x^{2})}^{2}}{{(y^{3})}^{2}} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

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

$\frac{9 {(x^{2})}^{2}}{{(y^{3})}^{2}} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

$\frac{9 x^{2 \cdot 2}}{{(y^{3})}^{2}} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 5.2.2

Multiply $2$ by $2$ .

$\frac{9 x^{4}}{{(y^{3})}^{2}} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 6

Apply basic rules of exponents.

Tap for more steps...

Step 6.1

Multiply the exponents in ${(y^{3})}^{2}$ .

Tap for more steps...

Step 6.1.1

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

$\frac{9 x^{4}}{y^{3 \cdot 2}} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 6.1.2

Multiply $3$ by $2$ .

$\frac{9 x^{4}}{y^{6}} \cdot {(x^{2} y^{4})}^{\frac{1}{2}}$

Step 6.2

Apply the product rule to $x^{2} y^{4}$ .

$\frac{9 x^{4}}{y^{6}} \cdot ({(x^{2})}^{\frac{1}{2}} {(y^{4})}^{\frac{1}{2}})$

Step 6.3

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

Tap for more steps...

Step 6.3.1

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

$\frac{9 x^{4}}{y^{6}} \cdot (x^{2 (\frac{1}{2})} {(y^{4})}^{\frac{1}{2}})$

Step 6.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.3.2.1

Cancel the common factor.

$\frac{9 x^{4}}{y^{6}} \cdot (x^{2 (\frac{1}{2})} {(y^{4})}^{\frac{1}{2}})$

Step 6.3.2.2

Rewrite the expression.

$\frac{9 x^{4}}{y^{6}} \cdot (x^{1} {(y^{4})}^{\frac{1}{2}})$

Step 7

Simplify.

$\frac{9 x^{4}}{y^{6}} \cdot (x {(y^{4})}^{\frac{1}{2}})$

Step 8

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

Tap for more steps...

Step 8.1

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

$\frac{9 x^{4}}{y^{6}} \cdot (x y^{4 (\frac{1}{2})})$

Step 8.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.2.1

Factor $2$ out of $4$ .

$\frac{9 x^{4}}{y^{6}} \cdot (x y^{2 (2) \frac{1}{2}})$

Step 8.2.2

Cancel the common factor.

$\frac{9 x^{4}}{y^{6}} \cdot (x y^{2 \cdot 2 \frac{1}{2}})$

Step 8.2.3

Rewrite the expression.

$\frac{9 x^{4}}{y^{6}} \cdot (x y^{2})$

Step 9

Cancel the common factor of $y^{2}$ .

Tap for more steps...

Step 9.1

Factor $y^{2}$ out of $y^{6}$ .

$\frac{9 x^{4}}{y^{2} y^{4}} \cdot (x y^{2})$

Step 9.2

Factor $y^{2}$ out of $x y^{2}$ .

$\frac{9 x^{4}}{y^{2} y^{4}} \cdot (y^{2} x)$

Step 9.3

Cancel the common factor.

$\frac{9 x^{4}}{y^{2} y^{4}} \cdot (y^{2} x)$

Step 9.4

Rewrite the expression.

$\frac{9 x^{4}}{y^{4}} \cdot x$

Step 10

Combine $\frac{9 x^{4}}{y^{4}}$ and $x$ .

$\frac{9 x^{4} x}{y^{4}}$

Step 11

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

$\frac{9 (x^{1} x^{4})}{y^{4}}$

Step 12

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

$\frac{9 x^{1 + 4}}{y^{4}}$

Step 13

Add $1$ and $4$ .

$\frac{9 x^{5}}{y^{4}}$