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Example: 16¼ × 16¼ × 16¼ × 16¼ = 16(¼+¼+¼+¼) = 16(1) = 16. So 16¼ used 4 times in a multiplication gives 16, and so 16¼ is a 4th root of 16. General Rule. It worked for ½, it worked with ¼, in fact it works generally: x 1/n = The n- th Root of x. In other words: A fractional exponent like 1/n means to take the n-th root: x 1/n = n√x.
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If we apply the rules of exponents, we can see how there are two possible ways to convert an expression with a fractional exponent into an expression in radical form.
For example, 4 2 = 4×4 = 16. Here, exponent 2 is a whole number. In the number, say x 1/y, x is the base and 1/y is the fractional exponent. In this article, we will discuss the concept of fractional exponents, and their rules, and learn how to solve them.
The above relations enable us to express radicals as fractional exponents and fractional exponents as radicals. EXAMPLES 1. root(5,3)=3^(1/5) 2. root(3,2^2)=2^(2/3) 3. root(x+3)=(x+3)^(1/2) 4. x^(4/5)=root(5,x^4) 5. 3x^(3/4)=3root(4,x^3) 6.
Example 1: Write √15 as an expression with fractional exponents. Solution: The index of √15 is 2, and we have 1 as the power of the radicand. Therefore, our fractional exponent is ½.
2 wrz 2024 · Write expressions with rational exponents in radical form. Write radical expressions with rational exponents. Perform operations and simplify expressions with rational exponents. Perform operations on radicals with different indices.
