smc-6213-05-Index Laws

Functions, 2ADV EQ-Bank 11

Express \(\dfrac{m^4\, n^{-3}}{m^{-2}\, n^2}\) with positive indices only. (1 mark)

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\(\dfrac{m^6}{n^5}\)

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\(\dfrac{m^4\, n^{-3}}{m^{-2}\, n^2}=m^{(4+2)}\, n^{(-3-2)}=m^6\, n^{-5}=\dfrac{m^6}{n^5}\)

Simplify \(\left(16p^8\right)^{\frac{3}{4}} \ ÷\ (2p)^3\). (2 marks)

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\(p^3\)

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\(\left(16^{\frac{1}{4}} \times p^{8 \times \frac{1}{4}}\right)^3 \ ÷\ 8 p^3\)	\(=\dfrac{\left(2 p^2\right)^3}{8 p^3}\)
	\(=\dfrac{8 p^6}{8 p^3}\)
	\(=p^3\)

Simplify \(\left(27x^6\right)^{\frac{1}{3}} \times(2x)^{-2}\). (2 marks)

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\(\dfrac{3}{4}\)

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\(\left(27 x^6\right)^{\frac{1}{3}} \times(2 x)^{-2}\)	\(=27^{\frac{1}{3}} \times x^{6 \times \frac{1}{3}} \times \dfrac{1}{4 x^2}\)
	\(=3 x^2 \times \dfrac{1}{4 x^2}\)
	\(=\dfrac{3}{4}\)

Simplify \(8ab^2 \times 2a^{-2}\). (2 marks)

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\(\dfrac{16b^2}{a}\)

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\(8ab^2 \times 2a^{-2}=8ab^2 \times \dfrac{2}{a^2}=\dfrac{16b^2}{a}\)

Simplify \(x^5 \ ÷ \ x^{-3}\). (1 mark)

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\(x^{8}\)

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\(x^5 \ ÷ \ x^{-3}=x^{(5-(-3))}=x^8\)

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

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`(p^2)/q`

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