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Indices Solutions

Attempt these in your workbooks

Question 1

math \dfrac{3x^5y^{-2}}{10x^{-1}y^3} \div \dfrac{6xy^3}{15x^4y^{-2}} \quad \; = \dfrac{3x^6}{10y^5} \div \dfrac{2y^5}{5x^3} math math . \qquad \qquad \qquad \qquad \qquad = \dfrac{3x^6}{10y^5} \times \dfrac{5x^3}{2y^5} math math . \qquad \qquad \qquad \qquad \qquad = \dfrac{3x^9}{4y^{10}} math

Question 2

math 27^{\frac{2}{3}} \quad = \Big( 3^3 \Big) ^{\frac{2}{3}} \qquad \textit{ raised to another power so multiply indices} math math \\ . \qquad \; = 3^2 \\ \\ . \qquad \; = 9 math

OR

math 27^{\frac{2}{3}} \quad = \Big( \sqrt[3]{27} \Big) ^2 \qquad \textit{ index of 1/3 is equivalent to cube root} math math \\ . \qquad \; = \big( 3 \big) ^2 \\ \\ . \qquad \; = 9 math

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