Algebra Examples

$\frac{x^{2} y^{2}}{3 x^{2} y} \cdot {(3 x^{4} y)}^{4} - 7 x^{16} y^{5}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Cancel the common factor.

$\frac{x^{2} y^{2}}{3 x^{2} y} \cdot {(3 x^{4} y)}^{4} - 7 x^{16} y^{5}$

Step 1.1.2

Rewrite the expression.

$\frac{y^{2}}{3 y} \cdot {(3 x^{4} y)}^{4} - 7 x^{16} y^{5}$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$\frac{y \cdot y}{3 y} \cdot {(3 x^{4} y)}^{4} - 7 x^{16} y^{5}$

Step 1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.2.1

Factor $y$ out of $3 y$ .

$\frac{y \cdot y}{y \cdot 3} \cdot {(3 x^{4} y)}^{4} - 7 x^{16} y^{5}$

Step 1.2.2.2

Cancel the common factor.

$\frac{y \cdot y}{y \cdot 3} \cdot {(3 x^{4} y)}^{4} - 7 x^{16} y^{5}$

Step 1.2.2.3

Rewrite the expression.

$\frac{y}{3} \cdot {(3 x^{4} y)}^{4} - 7 x^{16} y^{5}$

Step 1.3

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

Tap for more steps...

Step 1.3.1

Apply the product rule to $3 x^{4} y$ .

$\frac{y}{3} \cdot ({(3 x^{4})}^{4} y^{4}) - 7 x^{16} y^{5}$

Step 1.3.2

Apply the product rule to $3 x^{4}$ .

$\frac{y}{3} \cdot (3^{4} {(x^{4})}^{4} y^{4}) - 7 x^{16} y^{5}$

Step 1.4

Rewrite using the commutative property of multiplication.

$3^{4} \frac{y}{3} ({(x^{4})}^{4} y^{4}) - 7 x^{16} y^{5}$

Step 1.5

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.5.1

Factor $3$ out of $3^{4}$ .

$3 \cdot 3^{3} \frac{y}{3} ({(x^{4})}^{4} y^{4}) - 7 x^{16} y^{5}$

Step 1.5.2

Cancel the common factor.

$3 \cdot 3^{3} \frac{y}{3} ({(x^{4})}^{4} y^{4}) - 7 x^{16} y^{5}$

Step 1.5.3

Rewrite the expression.

$3^{3} y ({(x^{4})}^{4} y^{4}) - 7 x^{16} y^{5}$

Step 1.6

Multiply $y$ by $y^{4}$ by adding the exponents.

Tap for more steps...

Step 1.6.1

Move $y^{4}$ .

$3^{3} (y^{4} y) {(x^{4})}^{4} - 7 x^{16} y^{5}$

Step 1.6.2

Multiply $y^{4}$ by $y$ .

Tap for more steps...

Step 1.6.2.1

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

$3^{3} (y^{4} y^{1}) {(x^{4})}^{4} - 7 x^{16} y^{5}$

Step 1.6.2.2

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

$3^{3} y^{4 + 1} {(x^{4})}^{4} - 7 x^{16} y^{5}$

Step 1.6.3

Add $4$ and $1$ .

$3^{3} y^{5} {(x^{4})}^{4} - 7 x^{16} y^{5}$

Step 1.7

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

$27 y^{5} {(x^{4})}^{4} - 7 x^{16} y^{5}$

Step 1.8

Multiply the exponents in ${(x^{4})}^{4}$ .

Tap for more steps...

Step 1.8.1

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

$27 y^{5} x^{4 \cdot 4} - 7 x^{16} y^{5}$

Step 1.8.2

Multiply $4$ by $4$ .

$27 y^{5} x^{16} - 7 x^{16} y^{5}$

Step 2

Subtract $7 x^{16} y^{5}$ from $27 y^{5} x^{16}$ .

Tap for more steps...

Step 2.1

Move $y^{5}$ .

$27 x^{16} y^{5} - 7 x^{16} y^{5}$

Step 2.2

Subtract $7 x^{16} y^{5}$ from $27 x^{16} y^{5}$ .

$20 x^{16} y^{5}$