Basic Math Examples

${(\frac{4 y^{- 3}}{15 c y^{2}})}^{- 2} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 1

Move $y^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{4}{15 c y^{2} y^{3}})}^{- 2} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 2

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

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Step 2.1

Move $y^{3}$ .

${(\frac{4}{15 c (y^{3} y^{2})})}^{- 2} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 2.2

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

${(\frac{4}{15 c y^{3 + 2}})}^{- 2} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 2.3

Add $3$ and $2$ .

${(\frac{4}{15 c y^{5}})}^{- 2} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 3

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

${(\frac{15 c y^{5}}{4})}^{2} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{15 c y^{5}}{4}$ .

$\frac{{(15 c y^{5})}^{2}}{4^{2}} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 4.2

Apply the product rule to $15 c y^{5}$ .

$\frac{{(15 c)}^{2} {(y^{5})}^{2}}{4^{2}} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 4.3

Apply the product rule to $15 c$ .

$\frac{15^{2} c^{2} {(y^{5})}^{2}}{4^{2}} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 5

Simplify the numerator.

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Step 5.1

Raise $15$ to the power of $2$ .

$\frac{225 c^{2} {(y^{5})}^{2}}{4^{2}} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 5.2

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

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Step 5.2.1

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

$\frac{225 c^{2} y^{5 \cdot 2}}{4^{2}} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 5.2.2

Multiply $5$ by $2$ .

$\frac{225 c^{2} y^{10}}{4^{2}} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

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

$\frac{225 c^{2} y^{10}}{16} \cdot {(\frac{8 c y}{3 c^{2}})}^{2}$

Step 6.2

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

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Step 6.2.1

Factor $c$ out of $8 c y$ .

$\frac{225 c^{2} y^{10}}{16} \cdot {(\frac{c (8 y)}{3 c^{2}})}^{2}$

Step 6.2.2

Cancel the common factors.

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Step 6.2.2.1

Factor $c$ out of $3 c^{2}$ .

$\frac{225 c^{2} y^{10}}{16} \cdot {(\frac{c (8 y)}{c (3 c)})}^{2}$

Step 6.2.2.2

Cancel the common factor.

$\frac{225 c^{2} y^{10}}{16} \cdot {(\frac{c (8 y)}{c (3 c)})}^{2}$

Step 6.2.2.3

Rewrite the expression.

$\frac{225 c^{2} y^{10}}{16} \cdot {(\frac{8 y}{3 c})}^{2}$

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 $\frac{8 y}{3 c}$ .

$\frac{225 c^{2} y^{10}}{16} \cdot \frac{{(8 y)}^{2}}{{(3 c)}^{2}}$

Step 7.2

Apply the product rule to $8 y$ .

$\frac{225 c^{2} y^{10}}{16} \cdot \frac{8^{2} y^{2}}{{(3 c)}^{2}}$

Step 7.3

Apply the product rule to $3 c$ .

$\frac{225 c^{2} y^{10}}{16} \cdot \frac{8^{2} y^{2}}{3^{2} c^{2}}$

Step 8

Combine.

$\frac{225 c^{2} y^{10} (8^{2} y^{2})}{16 (3^{2} c^{2})}$

Step 9

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

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Step 9.1

Move $y^{2}$ .

$\frac{225 c^{2} (y^{2} y^{10}) \cdot 8^{2}}{16 (3^{2} c^{2})}$

Step 9.2

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

$\frac{225 c^{2} y^{2 + 10} \cdot 8^{2}}{16 (3^{2} c^{2})}$

Step 9.3

Add $2$ and $10$ .

$\frac{225 c^{2} y^{12} \cdot 8^{2}}{16 (3^{2} c^{2})}$

Step 10

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

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Step 10.1

Cancel the common factor.

$\frac{225 c^{2} y^{12} \cdot 8^{2}}{16 (3^{2} c^{2})}$

Step 10.2

Rewrite the expression.

$\frac{225 y^{12} \cdot 8^{2}}{16 \cdot (3^{2})}$

Step 11

Simplify the numerator.

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Step 11.1

Raise $8$ to the power of $2$ .

$\frac{225 y^{12} \cdot 64}{16 \cdot 3^{2}}$

Step 11.2

Multiply $64$ by $225$ .

$\frac{14400 y^{12}}{16 \cdot 3^{2}}$

Step 12

Reduce the expression by cancelling the common factors.

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Step 12.1

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

$\frac{14400 y^{12}}{16 \cdot 9}$

Step 12.2

Multiply $16$ by $9$ .

$\frac{14400 y^{12}}{144}$

Step 12.3

Cancel the common factor of $14400$ and $144$ .

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Step 12.3.1

Factor $144$ out of $14400 y^{12}$ .

$\frac{144 (100 y^{12})}{144}$

Step 12.3.2

Cancel the common factors.

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Step 12.3.2.1

Factor $144$ out of $144$ .

$\frac{144 (100 y^{12})}{144 (1)}$

Step 12.3.2.2

Cancel the common factor.

$\frac{144 (100 y^{12})}{144 \cdot 1}$

Step 12.3.2.3

Rewrite the expression.

$\frac{100 y^{12}}{1}$

Step 12.3.2.4

Divide $100 y^{12}$ by $1$ .

$100 y^{12}$