Question

Anyone know how to do these and explain so I can do the rest lol.

Answer 1

Answer:

B.

Step-by-step explanation:

For this, you want to know a few exponent rules. If you're multiplying two variables that are the same and have exponents, all you do is add up their exponents to get the product.

For example, a²a² = a^4. If it helps, you can write it out like (a·a)·(a·a) to help yourself see where a^4 comes from.

Next, if a variable has a negative exponent, it actually means this:

$a^(-2) = \frac{1}{a^{2} }$

So with your expression, you have m^(-6) * n^(-3) on top. There's no way to simplify this on it's own because m and n are different variables and can't be combined. But if you look on the bottom, you have more m's and n's, so what you can do is actually cancel out some stuff. Using the two exponent rules I gave you, you can see that m^(-13) can be rewritten as m^(-6) * m^(-7). You can write it as any combination of numbers so long as the sum of their exponents = -13, but I chose to break it into -6 and -7 because it'll let us cancel out the m^(-6) on the top. So:

$\frac{m^(-6)n^(-3)}{m^(-6)m^(-7)n^(-1)}$

And you can cancel out those m^(-6), which leaves you with

$\frac{n^(-3)}{m^(-7)n^(-1)}$

Now, see if you can cancel out the n's too. If you break n^(-3) into n^(-1) * n(-2), you can cancel out the n^(-1) on the top and bottom of the fraction, so you're left with

$\frac{n^(-2)}{m^(-7)}$

And lastly, since both of these variables have negative exponents, you can rewrite them as 1/n^(2) and 1/m^(7), and see that they simplify to choice B when you do that. (Or, if you're like me and that sounds like too much work, just know that if it's a negative exponent in the denominator, it can move up to the top and become a positive exponent. If it's a negative exponent in the numerator, it can move to the bottom to become a positive exponent. Either drop it down or move it up; it just needs to switch places.)

Answer 2

Answer:

Option B. m⁷/n²  is the correct answer.

Step-by-step explanation:

Identity,

xᵃ * xᵇ = xᵃ⁺ᵇ  

xᵃ/xᵇ = xᵃ⁻ᵇ

x⁻ᵃ = 1/xᵃ

It is given that,

m⁻⁶ n⁻³/m⁻¹³ n⁻¹

Using  these three identities we can write,

m⁻⁶ n⁻³/m⁻¹³ n⁻¹ = m⁻⁶ m¹³/n⁻¹n³   (since x⁻ᵃ = 1/xᵃ)

m⁻⁶ m¹³/n⁻¹n³ =m⁽⁻⁶⁺¹³⁾/n⁽⁻¹⁺³⁾ = m⁷/n²  (since xᵃ * xᵇ = xᵃ⁺ᵇ   and xᵃ/xᵇ = xᵃ⁻ᵇ)

Therefore Option B. m⁷/n² is the correct answer