smc-4228-55-Indices to powers

Indices, SMB-075

Simplify `(p/q)^3 ÷ (pq^(-2))`. (2 marks)

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`(p^2)/q`

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`(p/q)^3 ÷ (pq^(-2))`	`= (p^3)/(q^3) ÷ p/(q^2)`
	`= (p^3)/(q^3) xx (q^2)/p`
	`= (p^2)/q`

Indices, SMB-027

Simplify `(a(b^2)^3)/(a^2b)`. (2 marks)

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`b^5/a`

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`(a(b^2)^3)/(a^2b)`	`= (ab^6)/(a^2b)`
	`= b^5/a`

Indices, SMB-011

Simplify the expression `(5p^3)^2`. (2 marks)

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`25p^6`

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`(5p^3)^2`	`= 5^2 xx (p^3)^2`
	`= 25p^(3xx2)`
	`=25p^6`

Indices, SMB-010

Simplify the expression `(2x^3)^4`. (2 marks)

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`16x^12`

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`(2x^3)^4`	`= 2^4 xx (x^3)^4`
	`= 16x^(3xx4)`
	`=16x^12`