how do i set up and whats the prosedure to solve 10 to the 7th power times 10 to the third power divided by 10 to the 4th power times ten to the negitive 9the power? please help you are doing mankind a favor.if i don't pass this i will be labeld the dumest of the ed.
10^7 * 10^3
-------------
10^4 *10^-9
to multiply, add exponents if the base is the same.
Of course that means to divide, subtract exponents.
Since the base for all of these is ten, all we have to do is add and subtract.
7 + 3 - 4 - -9 of course - - is +
7 + 3 - 4 + 9 = 15
so the answer is :::
10^15
We have this:
10^7 * 10^3
------------- =
10^4 * 10^-9
We can multiply the numerators and denominators as step one, if you'd like.
10^7 * 10^3 = 10^10 = our numerator.
10^4 * 10^-9 = 10^-5 = our denominator.
We now have this fraction:
10^10/10^-5
Since we have the SAME BASE of 10 in the numerator and denominator, we simply SUBTRACT THE EXPONENTS.
Our exponents are:
10 - (-5) = 10 + 5 = 15
Final answer: 10^15, which is read:
"ten to the fifthteenth power."
The word power also means exponent, which also means degree.
Is that clear?
To solve the expression (10^7 × 10^3) / (10^4 × 10^-9), we can use the properties of exponents and simplify step by step. Let's break it down:
Step 1: Start with the numerator (10^7 × 10^3).
- When multiplying numbers with the same base, add their exponents.
- In this case, 10^7 × 10^3 becomes 10^(7+3).
Step 2: Simplify the numerator.
- 10^(7+3) equals 10^10.
Step 3: Move to the denominator (10^4 × 10^-9).
- When multiplying numbers with the same base, add their exponents.
- In this case, 10^4 × 10^-9 becomes 10^(4+(-9)).
Step 4: Simplify the denominator.
- 10^(4+(-9)) equals 10^(-5).
Step 5: Rewrite the expression with the simplified numerator and denominator.
- (10^10) / (10^(-5))
Step 6: When dividing numbers with the same base, subtract the exponents.
- In this case, 10^10 / 10^(-5) becomes 10^(10-(-5)).
Step 7: Simplify the division.
- 10^(10-(-5)) equals 10^(10+5).
Step 8: Final simplification.
- 10^(10+5) equals 10^15.
Therefore, the answer to the expression (10^7 × 10^3) / (10^4 × 10^-9) is 10^15.