Simplify and express each of the following in exponential form $\frac{(4^{5} \times a^{8} b^{3})}{(4^{5} \times a^{5} b^{2})} .$

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Solution

Simplification of $\frac{(4^{5} \times a^{8} b^{3})}{(4^{5} \times a^{5} b^{2})}$
$= \frac{(4^{5} \times a^{8} b^{3})}{(4^{5} \times a^{5} b^{2})}$
$= 4^{(5 - 5)} \times (a^{(8 - 5)} \times b^{(3 - 2)}) \dots [∵ a^{m} \div a^{n} = a^{(m - n)}]$
$= 4^{0} \times (a^{3} b)$
$= 1 \times a^{3} b$
$= a^{3} b$
Hence, the value of $\frac{(4^{5} \times a^{8} b^{3})}{(4^{5} \times a^{5} b^{2})}$ is $a^{3} b$

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Similar questions

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

\frac{3^{7}}{3^{4} \times 3^{3}}

\frac{4^{5} \times a^{8} b^{3}}{4^{5} \times a^{5} b^{2}}

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

\frac{4^{5} \times a^{3} b^{3}}{4^{5} \times a^{5} b^{2}}

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