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Exponents with Like Bases

ix Simplify a...

Question

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

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Solution

(ix) $\frac{2^{8} \times a^{5}}{4^{3} \times a^{3}} = \frac{2^{8} \times a^{5}}{(2^{2})^{3} \times a^{3}} = \frac{2^{8} \times a^{5}}{2^{6} \times a^{3}} [∵ (a^{m})^{n} = a^{m \times n}]$
$= 2^{8 - 6} \times a^{5 - 3} = 2^{2} \times a^{2} [∵ a^{m} \div a^{n} = a^{m - n}]$
$= (2 a)^{2} [∵ a^{m} \times b^{m} = (a \times b)^{m}]$

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Similar questions

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

Question 84 (d)

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

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

25^{4} \div 5^{3}

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

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