Algebra Examples

$- (8 x^{2} y^{0}) {(- 2 x^{5} z^{- 7})}^{2}$

Step 1

Anything raised to $0$ is $1$ .

$- 8 x^{2} \cdot 1 {(- 2 x^{5} z^{- 7})}^{2}$

Step 2

Multiply $- 8$ by $1$ .

$- 8 x^{2} {(- 2 x^{5} z^{- 7})}^{2}$

Step 3

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

$- 8 x^{2} {(- 2 x^{5} \frac{1}{z^{7}})}^{2}$

Step 4

Multiply $- 2 x^{5} \frac{1}{z^{7}}$ .

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Step 4.1

Combine $- 2$ and $\frac{1}{z^{7}}$ .

$- 8 x^{2} {(x^{5} \frac{- 2}{z^{7}})}^{2}$

Step 4.2

Combine $x^{5}$ and $\frac{- 2}{z^{7}}$ .

$- 8 x^{2} {(\frac{x^{5} \cdot - 2}{z^{7}})}^{2}$

Step 5

Move $- 2$ to the left of $x^{5}$ .

$- 8 x^{2} {(\frac{- 2 \cdot x^{5}}{z^{7}})}^{2}$

Step 6

Move the negative in front of the fraction.

$- 8 x^{2} {(- \frac{2 \cdot x^{5}}{z^{7}})}^{2}$

Step 7

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

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Step 7.1

Apply the product rule to $- \frac{2 x^{5}}{z^{7}}$ .

$- 8 x^{2} ({(- 1)}^{2} {(\frac{2 x^{5}}{z^{7}})}^{2})$

Step 7.2

Apply the product rule to $\frac{2 x^{5}}{z^{7}}$ .

$- 8 x^{2} ({(- 1)}^{2} \frac{{(2 x^{5})}^{2}}{{(z^{7})}^{2}})$

Step 7.3

Apply the product rule to $2 x^{5}$ .

$- 8 x^{2} ({(- 1)}^{2} \frac{2^{2} {(x^{5})}^{2}}{{(z^{7})}^{2}})$

Step 8

Simplify the expression.

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Step 8.1

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

$- 8 x^{2} (1 \frac{2^{2} {(x^{5})}^{2}}{{(z^{7})}^{2}})$

Step 8.2

Multiply $\frac{2^{2} {(x^{5})}^{2}}{{(z^{7})}^{2}}$ by $1$ .

$- 8 x^{2} \frac{2^{2} {(x^{5})}^{2}}{{(z^{7})}^{2}}$

Step 9

Simplify the numerator.

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Step 9.1

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

$- 8 x^{2} \frac{4 {(x^{5})}^{2}}{{(z^{7})}^{2}}$

Step 9.2

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 9.2.1

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

$- 8 x^{2} \frac{4 x^{5 \cdot 2}}{{(z^{7})}^{2}}$

Step 9.2.2

Multiply $5$ by $2$ .

$- 8 x^{2} \frac{4 x^{10}}{{(z^{7})}^{2}}$

Step 10

Multiply the exponents in ${(z^{7})}^{2}$ .

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Step 10.1

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

$- 8 x^{2} \frac{4 x^{10}}{z^{7 \cdot 2}}$

Step 10.2

Multiply $7$ by $2$ .

$- 8 x^{2} \frac{4 x^{10}}{z^{14}}$

Step 11

Multiply $- 8 x^{2} \frac{4 x^{10}}{z^{14}}$ .

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Step 11.1

Combine $- 8$ and $\frac{4 x^{10}}{z^{14}}$ .

$x^{2} \frac{- 8 (4 x^{10})}{z^{14}}$

Step 11.2

Multiply $4$ by $- 8$ .

$x^{2} \frac{- 32 x^{10}}{z^{14}}$

Step 11.3

Combine $x^{2}$ and $\frac{- 32 x^{10}}{z^{14}}$ .

$\frac{x^{2} (- 32 x^{10})}{z^{14}}$

Step 11.4

Multiply $x^{2}$ by $x^{10}$ by adding the exponents.

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Step 11.4.1

Move $x^{10}$ .

$\frac{x^{10} x^{2} \cdot - 32}{z^{14}}$

Step 11.4.2

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

$\frac{x^{10 + 2} \cdot - 32}{z^{14}}$

Step 11.4.3

Add $10$ and $2$ .

$\frac{x^{12} \cdot - 32}{z^{14}}$

Step 12

Move $- 32$ to the left of $x^{12}$ .

$\frac{- 32 \cdot x^{12}}{z^{14}}$

Step 13

Move the negative in front of the fraction.

$- \frac{32 x^{12}}{z^{14}}$