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

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Solution

Simplifying and expressing $\frac{(2^{8} \times a^{5})}{(4^{3} \times a^{3})}$ in the exponential form.
${(4)}^{3}$ can be expressed as $= {(2 \times 2)}^{3}$
$= {(2^{2})}^{3}$
$= {(2)}^{2 \times 3}$ $[∵ {(a^{m})}^{n} = a^{m n}]$
$= 2^{6}$
Now, $\frac{(2^{8} \times a^{5})}{(4^{3} \times a^{3})}$
$=$ $\frac{(2^{8} \times a^{5})}{(2^{6} \times a^{3})}$
$= 2^{8 - 6} \times a^{5 - 3}$ $[∵ a^{m} \div a^{n} = a^{m - n}]$
$= 2^{2} \times a^{2}$
$= {(2 a)}^{2}$ $[∵ (a^{m} \times b^{m} = {(a b)}^{m}]$
Therefore, $\frac{(2^{8} \times a^{5})}{(4^{3} \times a^{3})}$ $= {(2 a)}^{2}$ .

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

Question 84 (d)

Simplify and express each fo the following exponential form.
$(\frac{a^{6}}{a^{4}}) \times a^{5} \times a^{0}$

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

a^{5} \times a^{3} \times a^{7}

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