# Question #ec244

##### 2 Answers

#### Explanation:

We know that

Remember the rule of exponents:

#(a^b)^c = a^(bc)#

Therefore:

#(color(red)(5^-x))^(-3) = 5^((-x)(-3)) = 5^(3x)#

So we need to raise

#(color(red)(5^-x))^(-3) = color(blue)3^(-3) = 1/color(blue)3^3 = 1/27#

*Final Answer*

Or 0.37037....

#### Explanation:

In order to solve this, you can use a calculator or just use

However....if you don't know what

This might seem a little confusing at first, but the a is the "base". B is supposed to be the exponent of a in order to get

An actual example:

As you could see, 5 is the

Rule: If there is no base or a, then the a value is automatically assumed to be 10.

Now, another essential rule is that if a^b has an actual exponent on it (such as

Proof:

Now, let's multiply the result by two...

Let's multiply the result by two...

As you can see here,

Firstly,

Then, due to the rules of logarithms, we can move the power of the

Divide both sides by

Then multiply both sides by negative one to get:

Now that we know what x is, we can plug it into the equation to get...

You can simplify the logs with a calculator in order to get 0.37037....

Forgive me for this long answer.