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Exponents — MATHS STD 8 — Question

ICSE BoardEnglish MediumSTD 8MATHSExponents3 Marks
Question
Simplify: $8^{\frac{4}{3}}+25^{\frac{3}{2}}-\left(\frac{1}{27}\right)^{-\frac{2}{3}}$
✓

Answer

$ 8^{\frac{4}{3}}+25^{\frac{3}{2}}-\left(\frac{1}{27}\right)^{-\frac{2}{3}}$
$ =\left(2^3\right)^{\frac{4}{3}}+\left(5^2\right)^{\frac{3}{2}}-\left(\frac{1}{3^3}\right)^{-\frac{2}{3}}$
$ =2^{3 \times \frac{4}{3}}+5^{2 \times \frac{3}{2}}-\frac{1}{3^{3 \times\left(\frac{-2}{3}\right)}}$
$ =2^4+5^3-\frac{1}{3^{-2}}$
$ =16+125-3^2$
$ =141-9=132$
$ =2^{3 \times \frac{4}{3}}+5^{2 \times \frac{3}{2}}-\frac{1}{3^{3 \times\left(-\frac{2}{3}\right)}}$
$ =2^4+5^3-\frac{1}{3^{-2}}$
$ =16+125-3^2$
$ =141-9$
$=132$

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