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Exponents with Like Bases

c Evaluate 12...

Question

Question 85 (c)

Evaluate
$\frac{125 \times 5^{2} \times a^{7}}{10^{3} \times a^{4}}$

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Solution

We have
$\frac{125 \times 5^{2} \times a^{7}}{10^{3} \times a^{4}} = \frac{5^{3} \times 5^{2} \times a^{7}}{(2 \times 5)^{3} \times a^{4}} = \frac{5^{3 + 2} \times a^{7}}{2^{3} \times 5^{3} \times a^{4}} = \frac{5^{5} \times a^{7}}{2^{3} \times 5^{3} \times a^{4}} = \frac{5^{5 - 3 \times a^{7 - 4}}}{2^{3}} = \frac{5^{2} \times a^{3}}{2^{3}} = \frac{25 a^{3}}{8}$

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Question 85 (f)

Evaluate
$\frac{15^{4} \times 18^{3}}{3^{3} \times 5^{2} \times 12^{2}}$

a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}

are integers such that

\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}

0 \leq a < j

j = 2, 4, 5, 6, 7.

a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}

are intagers such that

\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}

0 \leq a_{j} < j

j = 2, 3, 4, 5, 6, 7

a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

Suppose $a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}$ are integers such that $\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}$ where 0 $\leq$ a< j for j= 2,4,5,6,7.

The sum $a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}$ is

Question 85 (a)

Evaluate
$\frac{7^{8} \times a^{10} b^{7} c^{12}}{7^{6} \times a^{8} b^{4} c^{12}}$

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Exponents with Like Bases

Standard VII Mathematics

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