Algebra Examples

${(\frac{4}{7} m)}^{2} (49 m) (17 p) (\frac{1}{34} p^{5})$

Step 1

Multiply $p$ by $p^{5}$ by adding the exponents.

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Step 1.1

Move $p^{5}$ .

${(\frac{4}{7} m)}^{2} (49 m) (17 (p^{5} p)) \frac{1}{34}$

Step 1.2

Multiply $p^{5}$ by $p$ .

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Step 1.2.1

Raise $p$ to the power of $1$ .

${(\frac{4}{7} m)}^{2} (49 m) (17 (p^{5} p^{1})) \frac{1}{34}$

Step 1.2.2

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

${(\frac{4}{7} m)}^{2} (49 m) (17 p^{5 + 1}) \frac{1}{34}$

Step 1.3

Add $5$ and $1$ .

${(\frac{4}{7} m)}^{2} (49 m) (17 p^{6}) \frac{1}{34}$

Step 2

Rewrite using the commutative property of multiplication.

$49 {(\frac{4}{7} m)}^{2} m (17 p^{6}) \frac{1}{34}$

Step 3

Combine $\frac{4}{7}$ and $m$ .

$49 {(\frac{4 m}{7})}^{2} m (17 p^{6}) \frac{1}{34}$

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 $\frac{4 m}{7}$ .

$49 \frac{{(4 m)}^{2}}{7^{2}} m (17 p^{6}) \frac{1}{34}$

Step 4.2

Apply the product rule to $4 m$ .

$49 \frac{4^{2} m^{2}}{7^{2}} m (17 p^{6}) \frac{1}{34}$

Step 5

Evaluate the exponents.

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Step 5.1

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

$49 \frac{16 m^{2}}{7^{2}} m (17 p^{6}) \frac{1}{34}$

Step 5.2

Raise $7$ to the power of $2$ .

$49 \frac{16 m^{2}}{49} m (17 p^{6}) \frac{1}{34}$

Step 6

Cancel the common factor of $49$ .

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Step 6.1

Cancel the common factor.

$49 \frac{16 m^{2}}{49} m (17 p^{6}) \frac{1}{34}$

Step 6.2

Rewrite the expression.

$16 m^{2} m (17 p^{6}) \frac{1}{34}$

Step 7

Multiply $m^{2}$ by $m$ by adding the exponents.

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Step 7.1

Move $m$ .

$16 (m \cdot m^{2}) (17 p^{6}) \frac{1}{34}$

Step 7.2

Multiply $m$ by $m^{2}$ .

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Step 7.2.1

Raise $m$ to the power of $1$ .

$16 (m^{1} m^{2}) (17 p^{6}) \frac{1}{34}$

Step 7.2.2

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

$16 m^{1 + 2} (17 p^{6}) \frac{1}{34}$

Step 7.3

Add $1$ and $2$ .

$16 m^{3} (17 p^{6}) \frac{1}{34}$

Step 8

Simplify the expression.

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Step 8.1

Rewrite using the commutative property of multiplication.

$16 \cdot 17 m^{3} p^{6} \frac{1}{34}$

Step 8.2

Multiply $16$ by $17$ .

$272 m^{3} p^{6} \frac{1}{34}$

Step 9

Cancel the common factor of $34$ .

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Step 9.1

Factor $34$ out of $272 m^{3} p^{6}$ .

$34 (8 m^{3} p^{6}) \frac{1}{34}$

Step 9.2

Cancel the common factor.

$34 (8 m^{3} p^{6}) \frac{1}{34}$

Step 9.3

Rewrite the expression.

$8 m^{3} p^{6}$