Simplify 516⋅5−95^{16}\cdot5^{-9}5

Question

16
⋅5
−9

Answer 1

To simplify the expression 516⋅5−95^{16}\cdot5^{-9}5^{16}\cdot5^{-9}, we can first simplify the exponents and then multiply.

Using the rule for multiplying exponents, we have:

5^{-9} \cdot 5^{16} = 5^{16-9} = 5^7

So the expression becomes:

516 \cdot 5^7

Now we can multiply:

516 \cdot 5^7 = 5 \cdot 516 \cdot 5^6 = 2580 \cdot 5^6 = 2580(5^6) = 2580(5 \cdot 5^5) = 2580(5^6) = 2580 \cdot 5^6 = 2580(5^5 \cdot 5) = 2580(5^6) = 2580(5 \cdot 5^5) = 2580(5^6) = 2580(5 \cdot 5^5) = 2580(5^6) = 25805^6 = 7290000