Question

please please please please please please please please please please please please please please please please please please please please please please please


with steps not useless things pls​

Answer 1

Answer:

$a) \frac{ {35}^{4} }{ ({5}^{2} ){}^{2} \times {7}^{4} } \div ({4}^{2} ) {}^{ - 2} \times \frac{1}{ {2}^{8} } + {2}^{0} - 2$

$\frac{(7 \times 5 {})^{4} }{5 {}^{4} \times {7}^{4} } \div {4}^{ - 4} \times \frac{1}{ {2}^{8} } + {2}^{0} - 2$

because (35=7×5) and we know that (a^n)^m= a^n×m

$\frac{ {5}^{4} \times {7}^{4} }{ {5}^{4} \times {7}^{4} } \div \frac{1}{ {4}^{4} } \times \frac{1}{ {2}^{8} } + 1 - 2$

because a^0=1

${5}^{4 - 4} \times {7}^{4 - 4} \div \frac{1}{ {(2)}^{4 \times 2} } \times \frac{1}{ {2}^{8} } - 1$

because 4= 2^2

${5}^{0} \times {7}^{0} \div \frac{1}{ {2}^{8} } \times \frac{1}{ {2}^{8} } - 1$

$1 \div \frac{1}{ {2}^{16} } - 1$

because a^n × a^m = a^n+m

$1 \div {2}^{ - 16} - 1$

$\frac{1}{2 {}^{ - 16} - 1} = \frac{2 {}^{ 16} }{ - 1} = ( - 2) {}^{16}$

because

${a}^{ - n} = \frac{1}{ {a}^{n} }$

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$b) \frac{ {24}^{5} }{ {3}^{4} \times 3 \times {2}^{20} }$

we know that 24 = 2^3×3

therefore

$\frac{ {(2 \times 2 \times 2 \times 3})^{5} }{ {3}^{4} \times 3 \times {2}^{20} }$

$\frac{ ({2}^{3} \times 3) {}^{5} }{ {3}^{4} \times 3 \times {2}^{20} } = \frac{ {2}^{15} \times {3}^{5} }{ {3}^{4} \times 3 \times {2}^{20} }$

$\frac{2 {}^{15 - 20} \times 3 {}^{5 - 5} }{}$

because

$\frac{ {a}^{n} }{ {a}^{m} } = {a}^{n - m}$

$= {2}^{ - 5} \times 1 = {2}^{ - 5}$