How do you simplify a expression with positive exponents?
How do you write a fractions an expression using a negative exponent?
I'll try to answer the case I think you're asking about. If I'm guessing wrong, do ask again.
If you have something like x^2 * x^3 (x-squared times x-cubed) then you add the exponents:
x^2 * x^3 = x^5
Similarly, in general,
x^a * x^b = x^(a+b)
With negative exponents, you drop the negative bit, and write "one over" the expression, thus:
x^(-1) = 1/x
x^(-2) = 1/x^2
x^(-3.14159) = 1/x^3.14159
and in general
x^(-a) = 1/x^a
like, the scientific notation?
Yes, but "scientific notation" is often used when talking about powers of 10, like:
20000 = 2 * 10^4
This makes arithmetic with large numbers easy, since, following the rule above, all you have to do is add powers to multiply the factors of 10, like:
(2.1 * 10^5) * (3 * 10^4)
= 2.1 * 3 * 10^5 * 10^4
= 6.1 * 10^9
Oops: that last line should have been
= 6.3 * 10^9
of course!
To simplify an expression with positive exponents, follow these steps:
1. Identify any exponents in the expression and determine their base.
2. Use the rules of exponents to simplify each term. The basic rules are as follows:
- If you have a term with a power raised to another power, multiply the exponents: (a^m)^n = a^(m * n).
- When multiplying terms with the same base, add the exponents: a^m * a^n = a^(m + n).
- When dividing terms with the same base, subtract the exponents: a^m / a^n = a^(m - n).
- If there is a negative exponent, you can move it to the denominator: a^(-n) = 1 / a^n.
- Any term raised to the power of zero is equal to 1: a^0 = 1.
For example, let's simplify the expression 2^3 * 2^2:
- Apply the multiplication rule: 2^(3 + 2) = 2^5 = 32.
To write a fraction as an expression using a negative exponent, follow these steps:
1. Identify the fraction you want to rewrite.
2. Express the fraction with the numerator or denominator as the base and the negative exponent as the reciprocal of the original exponent.
- If you have a fraction with a positive exponent in the numerator, you can rewrite it with a negative exponent in the denominator: a^m / b^n = a^m / b^n = a^m * b^(-n).
- If you have a fraction with a positive exponent in the denominator, you can rewrite it with a negative exponent in the numerator: a^m / b^n = a^m / b^n = a^m * b^(-n).
For example, let's rewrite the fraction 1 / x^3 with a negative exponent:
- Apply the negative exponent rule: 1 / x^3 = x^(-3).