Simplify the following expression.5^-3*5^4

Question

Simplify the following expression.5^-3*5^4

Answer 1

5^-3*5⁴

Here is another way that you should reflect on this one. There are two components to a number expressed in exponent form. Here, 5 is the BASE and -3 and 4 are the POWERS. 

Step 1: Whenever the BASE is the same for two numbers expressed in exponent form (like it is here), you should ADD the powers. 

Step 2: 5^-3*5⁴ = 5^(-3+4) = 5¹

So the answer is essentially 5. 

 

Answer 2

The problem posed is 5^-3*5⁴.

Now, 5⁴ is 5*5*5*5.

What, however, is 5^-3?0

Now, 5³ is 5*5*5

and 5² is 5*5.

Extending this, 5¹ is 5

and 5⁰ is 5/5 which is 1

So 5^-1 would be 1/5, 5^-2 would be 1/(5*5), and 5^-3 would be 1/(5*5*5).

So, 5^-3*5⁴ is (5*5*5*5)/(5*5*5) = 5.