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[latex]10{}^{-1}10^{3} = ?[/latex]
[latex]\frac{10{}^{3}}{10^{-2}} = ?[/latex]
[latex]100^{\frac{1}{2}} = ?[/latex]
[latex]100{}^{(1-n)} = 5[/latex]; What is n?
The 4th problem can be solved via LOGs. I didn't try to solve it. The first thing you do is to take the LOG of both sides.
To multiply, you add exponents.
If you can do this problem USING LOGS, we are there:
[latex]1.6^{3}+2.7{}^{3.2}[/latex]
This one is a really tough problem and there are two ways that I know to do it. I'd have to brush up on my skills to do it. I don't expect you to be able to do it.
I do see now, where some of this provides a foundation even though it's not normally used.
Your making up answers. The first three problems don't need to involve logs. Only exponent rules.
OK, the 100^(1/2) is really √100 or 10. The whole point is (1/3) power is cube root, 1/2 power is square root, 1/6 power is the sixth root etc.
Exponent rules. The bases MUST the same
MULTIPLY: Add exponents. Yea I tricked you. (10^2)*(10^2) may have been easier. That answer is: 10^4. 2+2 = 4.
I gave you exponents of-1 and 3, so -1+3=2 and the answer is 10^2.
DIVISION is Subtract exponents. Yea, I tricked you again. (3-(-2)) = 5, so the answer is 10^5. It's 1000/0.01=10^5
You could have used your trusty calculator to get these same answers. Try raising 100 to the 1/2 power and see if it's not the same as the sqrt(100) or 10.
Got it?
You ready to try Multiplying again.
Add exponents.
[latex]10^{5}10^{2}{/latex]
5+2 = 7 so it's [latex]10[l/atex]
It's like having 2 tens (10)(10) multiplied by 5 tens (10)(10)(10)(10)(10).
So you have 7 tens
[latex]\frac{1}{x^{n}}= x{}^{-n}[latex]
[latex]\frac{x^{3}}{x^{-2}} = x^{3}x^{2}[latex]
That's all that's happening.
Calculator:
You should have a button on your calculator labeled: [latex]x^{n}[/latex]
There are no parenthesis on my calculator.
To evaluate: 5-(1+3)/10
I would use 5 enter; 1 enter 3 enter + 10 divide -
There is a 4 level Stack in the calculator and one element is the display.
An enter "PUSHES" an item on the stack.
An operator like "+" operates on the last two items on the stack and puts the result in the display.
Past life comments: Basically I enjoy a challenge.
Muttley600 said:CBB is being quiet...