I really don't get this question:
10^-7x(1÷10^-5)+10^3-10^-1
To better understand this question, let's break it down step by step.
The question involves calculations with exponents and the order of operations. We'll simplify the expression following the rules of arithmetic.
Step 1: Simplify the expression within parentheses (1÷10^-5):
To divide by a negative exponent, we can rewrite it as a positive exponent:
1 ÷ 10^-5 = 1 ÷ (1/10^5) = 1 × 10^5 = 10^5
Step 2: Substitute the simplified value back into the expression:
10^-7x(10^5) + 10^3 - 10^-1
Step 3: Simplify the exponents:
Recall that when we multiply two numbers with the same base, we add the exponents:
10^-7 × 10^5 = 10^-7+5 = 10^-2
Now we have:
10^-2 + 10^3 - 10^-1
Step 4: Simplify once more:
To maintain a consistent base, we can rewrite 10^3 as 10^-3:
10^3 = 10^-3
Now we have:
10^-2 + 10^-3 - 10^-1
Step 5: Combine the terms with the same base by subtracting the exponents:
10^-2 - 10^-3 - 10^-1 = (10^-2 - 10^-3) - 10^-1
Step 6: Simplify each group of terms:
10^-2 - 10^-3 = (1/10^2) - (1/10^3) = 1/100 - 1/1000 = 10/1000 - 1/1000 = 9/1000
Now we have:
(9/1000) - 10^-1
Step 7: Simplify once more:
10^-1 = 1/10^1 = 1/10
Now we have:
(9/1000) - (1/10)
Step 8: Find a common denominator to combine the fractions:
The common denominator is 1000.
Converting (1/10) to have the same denominator:
(9/1000) - (1/10) = (9/1000) - (100/1000) = (9 - 100)/1000 = -91/1000
So, the final answer is -91/1000.