Question

What is the missing exponent? 8^-5/(8^-7)^2=8[ ]

Answer 1

@Nnesha help again please?

Answer 2

you need to know 2 exponent rules \[\huge\rm (x^m)^n=x^{m \times n}\]
and the 2nd one \[\huge\rm \frac{ x^m }{ x^n }=x^{m-n}\]when we divide same bases we should subtract their exponents

Answer 3

so for the first one it's -7 times 2

the second one is -5 times -7? @nnesha

Answer 4

first one is right
2nd one you should `subtract` their exponent not multiply them

Answer 5

\[\frac{ 8^{-5} }{ 8^{-7 \times 2} }\]
-7 times 2 = ?

Answer 6

-14?

Answer 7

yes right so \[\frac{ 8^{-5} }{ 8^{-14}}\]

Answer 8

now apply 2nd exponent rule

Answer 9

is it -11? I might be wrong

Answer 10

here is an example \[\huge\rm \frac{ 2^3 }{ 2^{-3} } =2^{3\color{ReD}{-}(-3)}\]

Answer 11

we should subtract their exponents but if the exponents at the denominator is negative then you should add \[\huge\rm \frac{ 2^3 }{ 2^{-3} } =2^{3\color{ReD}{-}(-3)} =2^{3+3}\]