Question

Please tell me the answer ​

Answer 1

Question :

Solve -

1. $\sf{ {2}^{ - 3} \times {2}^{ - 2} }$

2. $\sf{ {7}^{5} \times {7}^{ - 4} \times {7}^{ - 6} }$

Answer :

The Law of Exponents we will use here is :-

$\star\boxed{\sf\purple{a {}^{ - n} = \frac{1}{ {a}^{n} }} }$

1.

$\implies\tt{ {2}^{ - 3} \times {2}^{ - 2} }$

$\implies \tt{ \frac{1}{ {2}^{3} } \times \frac{1}{ {2}^{2} } }$

$\implies \tt{ \frac{1}{8} \times \frac{1}{4} }$

$\implies \tt{ \frac{1}{32} } \orange\bigstar$

2.

$\implies \tt{ {7}^{5} \times {7}^{ - 4} \times {7}^{ - 6} }$

$\implies \tt{16807 \times \frac{1}{ {7}^{4} } \times \frac{1}{ {7}^{6} } }$

$\implies \tt{ \cancel{16807} \times \frac{1}{2401} \times \frac{1}{ \cancel{117649} {}^{ \: \: 7}}}$

$\implies \tt{ \frac{1}{2401} \times \frac {1}{7} }$

$\implies \tt{ \frac{1}{16807} } \: \: or \: \: \frac{1}{ {7}^{5} } \orange \bigstar$

______________.....

Laws of Exponents :

• $\sf{ {a}^{m} \times {a}^{n} = {a}^{m + n} }$

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

• $\sf{( {a}^{m} ) {}^{n} = a {}^{mn} }$

• $\sf{ {a}^{m} \times {b}^{m} =(ab) {}^{m} }$

• $\sf{(ab) {}^{m} = {a}^{m} b {}^{m} }$

• $\sf{ (\frac{a}{b} ) {}^{m} = \frac{a {}^{m} }{b {}^{m} } }$

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

• $\sf{ {a}^{ 0} = 1 }$