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Exponents — MATHS STD 8 — Question

ICSE BoardEnglish MediumSTD 8MATHSExponents3 Marks
Question
Simplify and express as positive indice: $\left(a^{-2} b\right)^{\frac{1}{2}} \times\left(a b^{-3}\right)^{\frac{1}{3}}$
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Answer

$ \left(a^{-2} b\right)^{\frac{1}{2}} \times\left(a b^{-3}\right)^{\frac{1}{3}}$
$ =\left(a^{-2 \times \frac{1}{2}} \cdot b^{\frac{1}{2}}\right) \times\left(a^{\frac{1}{3}} b^{-3 \times \frac{1}{3}}\right)$
$ =a^{-1} b^{\frac{1}{2}} \times a^{\frac{1}{3}} b^{-1}$
$ =a^{-1+\frac{1}{3}} b^{\frac{1}{2}-1}$
$ =a^{\frac{-2}{3}} b^{\frac{-1}{2}}$
$ =\frac{1}{a^{\frac{2}{3}} b \frac{1}{2}}$

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