How do you simplify (-10)^5/ (-10)^9?

3 Answers
May 16, 2018

1/10^4 or 10^(-4)

Explanation:

x^a/x^b=x^(a-b)

May 16, 2018

\frac{1}{10000}

Explanation:

When, in a fraction, the same quantity appears as a multiplicative factor in both numerator and denominator, it can be simplified.

By multiplicative factor, I mean that you can simplify the 2's here:

\frac{cancel(2)x}{cancel(2)y} = \frac{x}{y}

but not here:

\frac{x+2}{y+2} \ne \frac{x}{y}

In your case, the factors stand alone, so they can be simplified. Just remember the very definition of power as reiterated multiplication to write (I'm setting x=-10 just for aestethic reasons) \frac{x^5}{x^9} as

\frac{x\cdotx\cdotx\cdotx\cdotx}{x\cdotx\cdotx\cdotx\cdotx\cdotx\cdotx\cdotx\cdotx}

As you can see, the same quantity x appears a lot of times in both numerator and denominator, and so it can be simplified:

\frac{\cancel(x)\cdot\cancel(x)\cdot\cancel(x)\cdot\cancel(x)\cdot\cancel(x)}{\cancel(x)\cdot\cancel(x)\cdot\cancel(x)\cdot\cancel(x)\cdot\cancel(x)\cdotx\cdotx\cdotx\cdotx}=\frac{1}{x^4}

So, the answer is

\frac{1}{(-10)^4}=\frac{1}{10000}

N.B.: in general, when you have the same quantity appearing in both numerator and denominator, you can simply perform some exponent algebra to get

\frac{x^a}{x^b}=x^{a-b}

the reason is exactly the reiterated multiplication cancelation that I just showed you. In this example, in fact, you had \frac{(-10)^5}{(-10)^9} = (-10)^{5-9} = (-10)^{-4}.

Negative exponent means to consider the inverse of the positive exponent, and in fact we have

(-10)^{-4} = \frac{1}{10^4}=\frac{1}{10000}.

May 16, 2018

1/10^4

Explanation:

Question: Simplify (-10)^5/(-10)^9

Using the index rule that a^n/a^m = a^(n-m), we can see that here a = -10, n = 5, and m = 9.

Our expression is now (-10)^(5-9) = (-10)^-4.

The next parts don't necessarily simplify the answer, but they make it a bit easier to visualise.

A negative power means we put one over our answer; think of it as a special case of the index rule above, but where n = 0.

Our expression is now 1/(-10)^4 and we're almost done.

We know that a number to an even power can be even or odd (like 2^2 = (-2)^2 = 4), so in this case we can write out answer as 1/10^4. Writing out all the zeros, this is 1/(10,000).