Simplify and express each of the following in exponential form-i 23 4 - 28- 212ii 82- 84 - 83iii 5752 - 53iv 54 - x 10 y 554 - x 7 y 4

We have (i) nbsp; (23)4 x 28 divide; 212 nbsp; nbsp; nbsp; = 212 x 28 divide; 212 nbsp; nbsp; nbsp; = 2(12 + 8) divide; 212 nbsp; ...

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Byju's Answer

Standard VII

Mathematics

Properties of Multiplication of Integers

Simplify and ...

Question

Simplify and express each of the following in exponential form:
(i) ${(2^{3})^{4} \times 2^{8}} \div 2^{12}$
(ii) (8² × 8⁴) ÷ 8³
(iii) $(\frac{5^{7}}{5^{2}}) \times 5^{3}$
(iv) $\frac{5^{4} \times x^{10} y^{5}}{5^{4} \times x^{7} y^{4}}$

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Solution

We have
(i) {(2³)⁴ x 2⁸} ÷ 2¹²
= {2¹² x 2⁸} ÷ 2¹²
= 2^{(12 + 8)} ÷ 2¹² = 2²⁰ ÷ 2¹²= 2^{(20 - 12)}= 2⁸

(ii) (8² x 8⁴) ÷ 8³
= 8^{(2 + 4)} ÷ 8³
= 8⁶ ÷ 8³
= 8^(6-3) = 8³ = (2³)³ = 2⁹

(iii) $(\frac{5^{7}}{5^{2}})$ x 5³ = 5^(7-2) x 5³
= 5⁵ x 5³
= 5^{(5 + 3 )} = 5⁸

(iv) $\frac{5^{4} \times x^{10} y^{5}}{5^{4} \times x^{7} y^{4}}$ = $5^{(4 - 4)} \times x^{(10 - 7)} \times y^{(5 - 4)}$
= $5^{0} \times x^{3} \times y$ [since 5⁰ = 1]
= $1 \times x^{3} y = x^{3} y$

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Similar questions

Q. Simplify and express each of the following in exponential form:

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

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

Question 84 (e)

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

Q. Simplify and express the following in exponential form:

(5^{4} \times m^{10} n^{5}) \div (5^{8} \times m^{7} n^{4})

Q. 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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Simplify and express each of the following in exponential form: (i) {(23)4×28}÷212 (ii) (82 × 84) ÷ 83 (iii) 5752×53 (iv) 54×x10y554× x7y4

Simplify and express each of the following in exponential form:
(i) ${(2^{3})^{4} \times 2^{8}} \div 2^{12}$
(ii) (8² × 8⁴) ÷ 8³
(iii) $(\frac{5^{7}}{5^{2}}) \times 5^{3}$
(iv) $\frac{5^{4} \times x^{10} y^{5}}{5^{4} \times x^{7} y^{4}}$