1/10^9x5^2(2)^5x6^2-4x6^-4/10^6/10^-6/10^15x100^5
Looks like a mess to me. Are the x's supposed to mean multiplication? Use parentheses to separate different terms.
Someone will be glad to critique your work
1/10^9.5^2(2)^2-4.6^-4/10^6/10^-6/10^15.100^5=
To simplify the given expression, let's break it down step by step:
1. Start by simplifying the exponents:
- In the numerator, we have (1/10^9) x 5^2 x (2)^5 x 6^2 - 4 x 6^(-4).
- In the denominator, we have 10^6 / 10^(-6) / 10^15 x 100^5.
2. Simplify the exponents in the numerator:
- 10^9 represents 10 raised to the power of 9.
- 5^2 represents 5 raised to the power of 2.
- (2)^5 represents 2 raised to the power of 5.
- 6^2 represents 6 raised to the power of 2.
- 6^(-4) represents 6 raised to the power of -4.
3. Simplify the exponents in the denominator:
- 10^6 represents 10 raised to the power of 6.
- 10^(-6) represents 10 raised to the power of -6.
- 10^15 represents 10 raised to the power of 15.
- 100^5 represents 100 raised to the power of 5.
4. Evaluate the numerator:
- (1/10^9) = 1 divided by 10 raised to the power of 9, which is a very small number close to 0.
- 5^2 = 5 x 5 = 25.
- (2)^5 = 2 x 2 x 2 x 2 x 2 = 32.
- 6^2 = 6 x 6 = 36.
- 4 x 6^(-4) = 4 x (1/6^4) = 4/6^4.
5. Evaluate the denominator:
- 10^6 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000.
- 10^(-6) = 1 / (10^6) = 1 / 1,000,000 = 0.000001.
- 10^15 = 10 x 10 x ... x 10 (15 times) = 1,000,000,000,000,000.
- 100^5 = 100 x 100 x 100 x 100 x 100 = 100,000,000.
6. Now substitute the simplified values back into the expression:
- Numerator: 1/10^9 x 5^2 x (2)^5 x 6^2 - 4 x 6^(-4) = (0) x 25 x 32 x 36 - 4/6^4 = 0 - 4/6^4.
- Denominator: 10^6 / 10^(-6) / 10^15 x 100^5 = 1,000,000 / 0.000001 / 1,000,000,000,000,000 x 100,000,000.
7. Simplify further using multiplication and division:
- In the numerator, we have 0 - 4/6^4 = -4/6^4. The negative sign shows that the result is negative.
- In the denominator, we have 1,000,000 / 0.000001 / 1,000,000,000,000,000 x 100,000,000 = 1,000,000,000,000,000 x 1,000,000 x 100,000,000.
- We can simplify the denominator by multiplying all the values together:
- 1,000,000,000,000,000 x 1,000,000 x 100,000,000 = 10^15 x 10^6 x 10^8 = 10^(15 + 6 + 8) = 10^29.
8. The final simplified expression is:
- Numerator: -4/6^4.
- Denominator: 10^29.
So, the simplified expression is -4/6^4 / 10^29.