Simplify (4/7m)^2(49m)(17p)(1/34p^5)

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

Step 1

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

Move $p^{5}$ .

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

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

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

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

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

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

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.

Apply the product rule to $\frac{4 m}{7}$ .

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

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.

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

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

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 $49$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

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

Move $m$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Step 8

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $16$ by $17$ .

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

Step 9

Cancel the common factor of $34$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (4/7m)^2(49m)(17p)(1/34p^5)

Related Questions

Support LCMGCF.com by disabling your adblocker.