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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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Similar questions

\frac{2^{3} \times 3^{4} \times 4}{3 \times 32}

Using laws of exponents, simplify and write the answer in exponential form:
$3^{2} \times 3^{4} \times 3^{8}$

Simplifyand express each of the following in exponential form:

(i) $\frac{2^{3} \times 3^{4} \times 4}{3 \times 32}$

(ii) $({5^{2}}^{3} \times 5^{4}) \div 5^{7}$

(iii) $25^{4} \div 5^{3}$

(iv) $\frac{3 \times 7^{2} \times 11^{8}}{21 \times 11^{3}}$

(v) $\frac{3^{7}}{3^{4} \times 3^{3}}$

(vi) $2^{0} + 3^{0} + 4^{0}$

(vii) $2^{0} \times 3^{0} \times 4^{0}$

(viii) $(3^{0} + 2^{0}) \times 5^{0}$

(ix) $\frac{2^{8} \times a^{5}}{4^{3} \times a^{3}}$

(x) $\frac{a^{5}}{a^{3}} \times a^{8}$

(xi) $\frac{4^{5} \times a^{8} b^{3}}{4^{5} \times a^{5} b^{2}}$

(xii) $(2^{3} \times 2)^{2}$

Express the following in exponential form:
$6 \times 6 \times 6 \times 6$

(2^{3} \times 2)^{2}

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