Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression.
How do the laws work with rational exponents? Provide a third expression to simplify that includes rational (fractional) exponents
what is your question? I will be happy to critique your thinking.
I don't understand, I'm struggling in math and I thought if I get an understanding of what kind of problems I was looking for, it would make things easier.
How about x^3 * x^4 = x^7
Can you not describe the rule I used by considering the meaning of powers such as x^3 ?
how about (x3)4 = x12 ?
Could you describe that law?
the basic laws of exponents work with any exponents, whether whole numbers, integers, rational or irrational.
Two laws of exponents are the product rule and the power rule:
1. Product Rule: When multiplying two exponential expressions with the same base, you can add their exponents.
Example: Simplify 2^3 * 2^4.
To use the product rule, keep the same base (2) and add the exponents (3+4).
2^3 * 2^4 = 2^(3+4) = 2^7 = 128.
2. Power Rule: When raising an exponential expression to a power, you can multiply the exponents.
Example: Simplify (5^2)^3.
Using the power rule, multiply the exponents.
(5^2)^3 = 5^(2*3) = 5^6 = 15625.
The laws of exponents also work with rational exponents. They follow similar rules as integer exponents, but the concept of fractional exponents involves taking roots.
Here's an example expression involving a rational exponent:
3^(2/3).
To simplify this expression, we can rewrite the fractional exponent as a radical expression. The numerator of the exponent is the power, and the denominator represents the root.
In this case, the numerator (2) is the power, and the denominator (3) is the root. So we want to find the cube root of 3 raised to the power of 2.
To simplify it further, we can evaluate the cube root of 3^2. The cube root of 3^2 is equivalent to the 2/3 power of 3.
Therefore, 3^(2/3) simplifies to the cube root of 3^2, which is the same as (cube root of 3)^2.