Algebra Examples

${(4 x^{2} y^{3})}^{- 2} {(- x^{10})}^{2}$

Step 1

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

$\frac{1}{{(4 x^{2} y^{3})}^{2}} {(- x^{10})}^{2}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $4 x^{2} y^{3}$ .

$\frac{1}{{(4 x^{2})}^{2} {(y^{3})}^{2}} {(- x^{10})}^{2}$

Step 2.2

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

$\frac{1}{4^{2} {(x^{2})}^{2} {(y^{3})}^{2}} {(- x^{10})}^{2}$

Step 2.3

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

$\frac{1}{16 {(x^{2})}^{2} {(y^{3})}^{2}} {(- x^{10})}^{2}$

Step 2.4

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

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Step 2.4.1

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

$\frac{1}{16 x^{2 \cdot 2} {(y^{3})}^{2}} {(- x^{10})}^{2}$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{1}{16 x^{4} {(y^{3})}^{2}} {(- x^{10})}^{2}$

Step 2.5

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

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Step 2.5.1

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

$\frac{1}{16 x^{4} y^{3 \cdot 2}} {(- x^{10})}^{2}$

Step 2.5.2

Multiply $3$ by $2$ .

$\frac{1}{16 x^{4} y^{6}} {(- x^{10})}^{2}$

Step 3

Simplify terms.

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Step 3.1

Apply the product rule to $- x^{10}$ .

$\frac{1}{16 x^{4} y^{6}} ({(- 1)}^{2} {(x^{10})}^{2})$

Step 3.2

Simplify the expression.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

${(- 1)}^{2} \frac{1}{16 x^{4} y^{6}} {(x^{10})}^{2}$

Step 3.2.2

Raise $- 1$ to the power of $2$ .

$1 \frac{1}{16 x^{4} y^{6}} {(x^{10})}^{2}$

Step 3.2.3

Multiply $\frac{1}{16 x^{4} y^{6}}$ by $1$ .

$\frac{1}{16 x^{4} y^{6}} {(x^{10})}^{2}$

Step 3.2.4

Multiply the exponents in ${(x^{10})}^{2}$ .

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Step 3.2.4.1

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

$\frac{1}{16 x^{4} y^{6}} x^{10 \cdot 2}$

Step 3.2.4.2

Multiply $10$ by $2$ .

$\frac{1}{16 x^{4} y^{6}} x^{20}$

Step 3.3

Cancel the common factor of $x^{4}$ .

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Step 3.3.1

Factor $x^{4}$ out of $16 x^{4} y^{6}$ .

$\frac{1}{x^{4} (16 y^{6})} x^{20}$

Step 3.3.2

Factor $x^{4}$ out of $x^{20}$ .

$\frac{1}{x^{4} (16 y^{6})} (x^{4} x^{16})$

Step 3.3.3

Cancel the common factor.

$\frac{1}{x^{4} (16 y^{6})} (x^{4} x^{16})$

Step 3.3.4

Rewrite the expression.

$\frac{1}{16 y^{6}} x^{16}$

Step 3.4

Combine $\frac{1}{16 y^{6}}$ and $x^{16}$ .

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