Simplify:
3x (to the -2 power)
2x(3rd power)times x(to the -2 power) times x(to the 7 power)
3x (to the negative 3 power) times (-4 power)
I searched Google under the key words "math power" and "math power negative" to get these possible sources:
http://www.homeschoolmath.net/teaching/zero-exponent-proof.php
http://www.math.com/school/subject2/lessons/S2U2L2DP.html
http://oakroadsystems.com/math/expolaws.htm
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
b(to the 9th power)x(b to the 9th power)
To simplify each expression, we can apply the properties of exponents:
1. Simplifying 3x^(-2):
When a number or variable is raised to a negative power, we can rewrite it as the reciprocal of the positive power. So, 3x^(-2) can be written as 3/(x^2), which is the simplified form.
2. Simplifying 2x^3 * x^(-2) * x^7:
To multiply terms with the same base, we add their exponents. Therefore, 2x^3 * x^(-2) * x^7 can be simplified as 2x^(3 + (-2) + 7) which becomes 2x^8.
3. Simplifying 3x^(-3) * (-4)^(-1):
Using the property of negative exponents, we can rewrite x^(-3) as 1/(x^3). So, 3x^(-3) * (-4)^(-1) becomes 3 * 1/(x^3) * 1/(-4). This simplifies to -3/(4x^3).
Hence, the simplified forms of the given expressions are:
1. 3x^(-2) = 3/(x^2)
2. 2x^3 * x^(-2) * x^7 = 2x^8
3. 3x^(-3) * (-4)^(-1) = -3/(4x^3)
To simplify each of these expressions, we can follow the basic rules of exponents.
1. Simplifying 3x^(-2):
To simplify this expression, we use the rule that states any non-zero number raised to the power of -n is equal to 1 divided by the number raised to the power of n. Therefore, 3x^(-2) becomes 3 / x^2.
2. Simplifying 2x^3 * x^(-2) * x^7:
To simplify this expression, we use the rule that states when multiplying variables with the same base, we add their exponents. Therefore, 2x^3 * x^(-2) * x^7 becomes 2 * x^(3 + -2 + 7) = 2x^8.
3. Simplifying 3x^(-3) * (-4)^(-1):
To simplify this expression, we apply the above-mentioned rule for negative exponents. Therefore, 3x^(-3) * (-4)^(-1) becomes 3 / x^3 * (-1 / 4) = -3 / (4x^3).
So, the simplified expressions are:
1. 3x^(-2) = 3 / x^2
2. 2x^3 * x^(-2) * x^7 = 2x^8
3. 3x^(-3) * (-4)^(-1) = -3 / (4x^3)