5 Marks Questions

Question 15 Marks

Simplify : $\frac{{{3^{ - 5}} \times {{10}^{ - 5}} \times 125}}{{{5^{ - 7}} \times {6^{ - 5}}}}$

Answer

$\frac{{{3^{ - 5}} \times {{10}^{ - 5}} \times 125}}{{{5^{ - 7}} \times {6^{ - 5}}}}$
$ = \frac{{{3^{ - 5}} \times {{(2 \times 5)}^{ - 5}} \times (5 \times 5 \times 5)}}{{{5^{ - 7}} \times {{(2 \times 3)}^{ - 5}}}}$
$ = \frac{{{3^{ - 5}} \times {2^{ - 5}} \times {5^{ - 5}} \times {5^3}}}{{{5^{ - 7}} \times {2^{ - 5}} \times {3^{ - 5}}}}$
$ = \frac{{{5^{ - 5}} \times {5^3}}}{{{5^{ - 7}}}}$
$ = \frac{{{5^{(5) + 3}}}}{{{5^{ - 7}}}}$
$ = \frac{{{5^{ - 2}}}}{{{5^{ - 7}}}}$
$ =5^{(-2)-(-7)} $
$ =5^{-2+7} $
$ =5^5 $

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Question 25 Marks

Simplify :$\frac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 8}}}}(t \ne 0)$

Answer

$\frac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 8}}}}(t \ne 0)$
$\frac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 8}}}}$
$ = \frac{{25 \times \frac{1}{{{t^4}}}}}{{\frac{1}{{{5^3}}} \times 10 \times \frac{1}{{{t^8}}}}}$
$ = \frac{{\frac{{25}}{{{t^4}}}}}{{\frac{1}{{125}} \times 10 \times \frac{1}{{{t^8}}}}}$
$ = \frac{{\frac{{25}}{{{t^4}}}}}{{\frac{{25}}{{25{t^8}}}}}$
$ = \frac{{25}}{{{t^4}}} \times \frac{{25{t^8}}}{2}$
$ = \frac{{625{t^{8 - 4}}}}{2}$
$ = \frac{{625}}{2}{t^4}$

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