Simplify 10abc^2 square root of 49a^2b^2c^2

$10 a b c^{2} \sqrt{49 a^{2} b^{2} c^{2}}$

Step 1

Rewrite $49 a^{2} b^{2} c^{2}$ as ${(7 a b c)}^{2}$ .

$10 a b c^{2} \sqrt{{(7 a b c)}^{2}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$10 a b c^{2} (7 a b c)$

Step 3

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$10 (a \cdot a) b c^{2} (7 b c)$

Multiply $a$ by $a$ .

$10 a^{2} b c^{2} (7 b c)$

Step 4

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$10 a^{2} (b \cdot b) c^{2} (7 c)$

Multiply $b$ by $b$ .

$10 a^{2} b^{2} c^{2} (7 c)$

Step 5

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

Move $c$ .

$10 a^{2} b^{2} (c \cdot c^{2}) \cdot 7$

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

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

$10 a^{2} b^{2} (c^{1} c^{2}) \cdot 7$

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

$10 a^{2} b^{2} c^{1 + 2} \cdot 7$

Add $1$ and $2$ .

$10 a^{2} b^{2} c^{3} \cdot 7$

Step 6

Multiply $7$ by $10$ .

$70 a^{2} b^{2} c^{3}$