Question

Simplify laws of exponents 4^-5 ×- 4^2​

Answer 1

${4}^{ - 5} \times {4}^{ - 2}$

we know that,

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

${4}^{ - 5} = \frac{1}{ {4}^{5} }$

${4}^{ - 2} = \frac{1}{ {4}^{2} }$

$\frac{1}{ {4}^{5} } \times \frac{1}{ {4}^{2} }$

using exponential law,

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

$\frac{1}{ {4}^{5 + 2} } = \frac{1}{ {4}^{7} }$

you could also do,

${4}^{ - 5} \times {4}^{ - 2} = {4}^{ - 5 + - 2}$

$= {4}^{ - 7}$

then apply

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

${4}^{ - 7} = \frac{1}{ {4}^{7} }$

Hope it helps

have a great day