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Exponents with Unlike Bases and Same Exponent

Question 2i S...

Question

Question 2(i)
Simplify and express each of the following in exponential form:
(i) $\frac{2^{3} \times 3^{4} \times 4}{3 \times 32}$

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Solution

(i) $\frac{2^{3} \times 3^{4} \times 4}{3 \times 32} = \frac{2^{3} \times 3^{4} \times 2^{2}}{3 \times 2^{5}} = \frac{2^{3 + 2} \times 3^{4}}{3 \times 2^{5}} [∵ a^{m} \times a^{n} = a^{m + n}]$
$= \frac{2^{5} \times 3^{4}}{3 \times 2^{5}} = 2^{5 - 5} \times 3^{4 - 1} [∵ a^{m} \div a^{n} = a^{m - n}]$
$= 2^{0} \times 3^{3} = 1 \times 3^{3} = 3^{3}$

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Q. Simplify and express the following in exponential form:
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\frac{2^{3} \times 3^{4} \times 4}{3 \times 32}

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Exponents with Unlike Bases and Same Exponent

Standard VI Mathematics

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