Finite Math Examples

$(5 x^{3} y) {(4 x^{- 2} y^{3})}^{- 2} {(2 x y)}^{0}$

Step 1

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

$5 x^{3} y {(4 \frac{1}{x^{2}} y^{3})}^{- 2} {(2 x y)}^{0}$

Step 2

Combine $4$ and $\frac{1}{x^{2}}$ .

$5 x^{3} y {(\frac{4}{x^{2}} y^{3})}^{- 2} {(2 x y)}^{0}$

Step 3

Combine $\frac{4}{x^{2}}$ and $y^{3}$ .

$5 x^{3} y {(\frac{4 y^{3}}{x^{2}})}^{- 2} {(2 x y)}^{0}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$5 x^{3} y {(\frac{x^{2}}{4 y^{3}})}^{2} {(2 x y)}^{0}$

Step 5

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

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Step 5.1

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

$5 x^{3} y \frac{{(x^{2})}^{2}}{{(4 y^{3})}^{2}} {(2 x y)}^{0}$

Step 5.2

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

$5 x^{3} y \frac{{(x^{2})}^{2}}{4^{2} {(y^{3})}^{2}} {(2 x y)}^{0}$

Step 6

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

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Step 6.1

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

$5 x^{3} y \frac{x^{2 \cdot 2}}{4^{2} {(y^{3})}^{2}} {(2 x y)}^{0}$

Step 6.2

Multiply $2$ by $2$ .

$5 x^{3} y \frac{x^{4}}{4^{2} {(y^{3})}^{2}} {(2 x y)}^{0}$

Step 7

Simplify the denominator.

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Step 7.1

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

$5 x^{3} y \frac{x^{4}}{16 {(y^{3})}^{2}} {(2 x y)}^{0}$

Step 7.2

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

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Step 7.2.1

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

$5 x^{3} y \frac{x^{4}}{16 y^{3 \cdot 2}} {(2 x y)}^{0}$

Step 7.2.2

Multiply $3$ by $2$ .

$5 x^{3} y \frac{x^{4}}{16 y^{6}} {(2 x y)}^{0}$

Step 8

Simplify terms.

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Step 8.1

Cancel the common factor of $y$ .

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Step 8.1.1

Factor $y$ out of $5 x^{3} y$ .

$y (5 x^{3}) \frac{x^{4}}{16 y^{6}} {(2 x y)}^{0}$

Step 8.1.2

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

$y (5 x^{3}) \frac{x^{4}}{y (16 y^{5})} {(2 x y)}^{0}$

Step 8.1.3

Cancel the common factor.

$y (5 x^{3}) \frac{x^{4}}{y (16 y^{5})} {(2 x y)}^{0}$

Step 8.1.4

Rewrite the expression.

$5 x^{3} \frac{x^{4}}{16 y^{5}} {(2 x y)}^{0}$

Step 8.2

Combine $5$ and $\frac{x^{4}}{16 y^{5}}$ .

$x^{3} \frac{5 x^{4}}{16 y^{5}} {(2 x y)}^{0}$

Step 8.3

Combine $x^{3}$ and $\frac{5 x^{4}}{16 y^{5}}$ .

$\frac{x^{3} (5 x^{4})}{16 y^{5}} {(2 x y)}^{0}$

Step 9

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

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Step 9.1

Move $x^{4}$ .

$\frac{x^{4} x^{3} \cdot 5}{16 y^{5}} {(2 x y)}^{0}$

Step 9.2

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

$\frac{x^{4 + 3} \cdot 5}{16 y^{5}} {(2 x y)}^{0}$

Step 9.3

Add $4$ and $3$ .

$\frac{x^{7} \cdot 5}{16 y^{5}} {(2 x y)}^{0}$

Step 10

Move $5$ to the left of $x^{7}$ .

$\frac{5 \cdot x^{7}}{16 y^{5}} {(2 x y)}^{0}$

Step 11

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

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Step 11.1

Apply the product rule to $2 x y$ .

$\frac{5 x^{7}}{16 y^{5}} ({(2 x)}^{0} y^{0})$

Step 11.2

Apply the product rule to $2 x$ .

$\frac{5 x^{7}}{16 y^{5}} (2^{0} x^{0} y^{0})$

Step 12

Simplify the expression.

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Step 12.1

Rewrite using the commutative property of multiplication.

$2^{0} \frac{5 x^{7}}{16 y^{5}} (x^{0} y^{0})$

Step 12.2

Anything raised to $0$ is $1$ .

$1 \frac{5 x^{7}}{16 y^{5}} (x^{0} y^{0})$

Step 12.3

Multiply $\frac{5 x^{7}}{16 y^{5}}$ by $1$ .

$\frac{5 x^{7}}{16 y^{5}} (x^{0} y^{0})$

Step 13

Cancel the common factor of $y^{0}$ .

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Step 13.1

Factor $y^{0}$ out of $16 y^{5}$ .

$\frac{5 x^{7}}{y^{0} (16 y^{5})} (x^{0} y^{0})$

Step 13.2

Factor $y^{0}$ out of $x^{0} y^{0}$ .

$\frac{5 x^{7}}{y^{0} (16 y^{5})} (y^{0} x^{0})$

Step 13.3

Cancel the common factor.

$\frac{5 x^{7}}{y^{0} (16 y^{5})} (y^{0} x^{0})$

Step 13.4

Rewrite the expression.

$\frac{5 x^{7}}{16 y^{5}} x^{0}$

Step 14

Combine $\frac{5 x^{7}}{16 y^{5}}$ and $x^{0}$ .

$\frac{5 x^{7} x^{0}}{16 y^{5}}$

Step 15

Multiply $x^{7}$ by $x^{0}$ by adding the exponents.

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Step 15.1

Move $x^{0}$ .

$\frac{5 (x^{0} x^{7})}{16 y^{5}}$

Step 15.2

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

$\frac{5 x^{0 + 7}}{16 y^{5}}$

Step 15.3

Add $0$ and $7$ .

$\frac{5 x^{7}}{16 y^{5}}$