Algebra Examples

${(4 x^{3} y^{6})}^{- 2} + {(2 x^{2} y^{4})}^{- 3}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

$\frac{1}{{(4 x^{3} y^{6})}^{2}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.2

Simplify the denominator.

Tap for more steps...

Step 1.2.1

Apply the product rule to $4 x^{3} y^{6}$ .

$\frac{1}{{(4 x^{3})}^{2} {(y^{6})}^{2}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.2.2

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

$\frac{1}{4^{2} {(x^{3})}^{2} {(y^{6})}^{2}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.2.3

Raise $4$ to the power of $2$ .

$\frac{1}{16 {(x^{3})}^{2} {(y^{6})}^{2}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.2.4

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

Tap for more steps...

Step 1.2.4.1

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

$\frac{1}{16 x^{3 \cdot 2} {(y^{6})}^{2}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.2.4.2

Multiply $3$ by $2$ .

$\frac{1}{16 x^{6} {(y^{6})}^{2}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.2.5

Multiply the exponents in ${(y^{6})}^{2}$ .

Tap for more steps...

Step 1.2.5.1

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

$\frac{1}{16 x^{6} y^{6 \cdot 2}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.2.5.2

Multiply $6$ by $2$ .

$\frac{1}{16 x^{6} y^{12}} + {(2 x^{2} y^{4})}^{- 3}$

Step 1.3

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

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{{(2 x^{2} y^{4})}^{3}}$

Step 1.4

Simplify the denominator.

Tap for more steps...

Step 1.4.1

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

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{{(2 x^{2})}^{3} {(y^{4})}^{3}}$

Step 1.4.2

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

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{2^{3} {(x^{2})}^{3} {(y^{4})}^{3}}$

Step 1.4.3

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

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{8 {(x^{2})}^{3} {(y^{4})}^{3}}$

Step 1.4.4

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

Tap for more steps...

Step 1.4.4.1

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

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{8 x^{2 \cdot 3} {(y^{4})}^{3}}$

Step 1.4.4.2

Multiply $2$ by $3$ .

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{8 x^{6} {(y^{4})}^{3}}$

Step 1.4.5

Multiply the exponents in ${(y^{4})}^{3}$ .

Tap for more steps...

Step 1.4.5.1

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

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{8 x^{6} y^{4 \cdot 3}}$

Step 1.4.5.2

Multiply $4$ by $3$ .

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{8 x^{6} y^{12}}$

Step 2

To write $\frac{1}{8 x^{6} y^{12}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{16 x^{6} y^{12}} + \frac{1}{8 x^{6} y^{12}} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $16 x^{6} y^{12}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{1}{8 x^{6} y^{12}}$ by $\frac{2}{2}$ .

$\frac{1}{16 x^{6} y^{12}} + \frac{2}{8 x^{6} y^{12} \cdot 2}$

Step 3.2

Multiply $2$ by $8$ .

$\frac{1}{16 x^{6} y^{12}} + \frac{2}{16 x^{6} y^{12}}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 2}{16 x^{6} y^{12}}$

Step 5

Add $1$ and $2$ .

$\frac{3}{16 x^{6} y^{12}}$