Question

Simplify3³×9²×125³÷9³

Answer 1

Step-by-step explanation:

3³×9²×125³÷9³

3×9³×5⁶÷9³

3 ×5⁶

=46875

Answer 2

Answer:

Step-by-step explanation:

Prime factorize 9 and 125

9 =  3* 3 = 3²

125 = 5 * 5 * 5 = 5³

3³ * 9² * 125³ ÷ 9³ = $\frac{3^{3}*(3^{2})^{2}*(5^{3})^{3}}{(3^{2})^{3}}$

                            $= \frac{3^{3}*3^{4}*5^{9}}{3^{6}}\\\\=\frac{3^{3+4}*5^{9}}{3^{6}}\\\\= \frac{3^{7}*5^{9}}{3^{6}}\\\\=3^{7-6}*5^{9}\\=3*5^{9}$

Exponent laws:

$(a^{m})^{n}=a^{m*n}\\\\\\a^{m}*a^{n} = a^{m +n}\\\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \ ; \ m > n$