Multiply Indices 4

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Question 1 of 3

Simplify

`5m^(-2) n^4 xx 3m^6 n^(-3)`

Question 2 of 3

Simplify

`(6xy^4)(-2x^3 y^2)`

Question 3 of 3

Simplify

`(7a^3)(-3a^3 b^2)(2/7ab^5)`

$$\color{#00880A}{5}^1 \times \color{#00880A}{3}^1 \times \color{#9a00c7}{m}^{-2} \times \color{#9a00c7}{m}^6 \times \color{#e65021}{n}^4 \times \color{#e65021}{n}^{-3}$$	`=`	$$\color{#00880A}{15} \times \color{#9a00c7}{m}^{(-2)+6} \times \color{#e65021}{n}^{4+(-3)}$$
	`=`	`15m^4 n`

$$\color{#00880A}{6}^1 \times (\color{#00880A}{-2})^1 \times \color{#9a00c7}{x}^1 \times \color{#9a00c7}{x}^3 \times \color{#e65021}{y}^4 \times \color{#e65021}{y}^2$$	`=`	$$\color{#00880A}{-12} \times \color{#9a00c7}{x}^{1+3} \times \color{#e65021}{y}^{4+2}$$
	`=`	`-12x^4 y^6`

$$\color{#00880A}{7}^1 \times (\color{#00880A}{-3})^1 \times \left(\color{#00880A}{\frac{2}{7}}\right)^1 \times \color{#9a00c7}{a}^3 \times \color{#9a00c7}{a}^3 \times \color{#9a00c7}{a}^1 \times \color{#e65021}{b}^2 \times \color{#e65021}{b}^5$$	`=`	$$\color{#00880A}{-3 \times 2} \times \color{#9a00c7}{a}^{3+3+1} \times \color{#e65021}{b}^{2+5}$$	`7 xx 1/7` cancels out

	`=`	`-6a^7 b^7`

		`5m^(-2) n^4 xx 3m^6 n^(-3)`
	`=`	`5 xx 3 xx m^(-2) xx m^6 xx n^4 xx n^(-3)`

		`(6xy^4)(-2x^3 y^2)`
	`=`	`(6 xx (-2)) xx (m xx x^3) xx (y^4 xx y^2)`