Question

5 to the power of 6 x 125 to the power of -3

Answer 1

Step-by-step explanation:

$\colorbox{purple}{greetings}$

Your question:

$= {5}^{6} \times {125}^{ - 3}$

Your answer:

$= {5}^{6} \times (5 {)}^{ - 3 \times 3}$

[ cube out 125 and multiply 3 to -3 ]

$= ( {5)}^{6 + ( - 9)}$

[ use the identity: a^m * a^n ]

$= {(5)}^{6 - 9}$

[ do the mathematical functions ]

$= {(5)}^{ - 3}$

$= \frac{1}{ {5}^{3} }$

[ reciprocal the number using this identity: a^-m = 1/a^m ]

$= \frac{1}{125}$

$\color{yellow}{final \: answer}$

$\frac{1}{125}$

Brainly Extra:

$1) {a}^{m} \times {a}^{n} = ( {a)}^{m + n}$

$2) {a}^{m} \times {b}^{m} = (a \times b {)}^{m}$

$3) {a}^{ - m} = \frac{ 1}{ {a}^{m} }$