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

1. anonymous

@Nnesha help again please?

2. Nnesha

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

3. anonymous

so for the first one it's -7 times 2 the second one is -5 times -7? @nnesha

4. Nnesha

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

5. Nnesha

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

6. anonymous

-14?

7. Nnesha

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

8. Nnesha

now apply 2nd exponent rule

9. anonymous

is it -11? I might be wrong

10. Nnesha

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

11. Nnesha

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