Girly Mphathobe
4 hours ago
Simplify fractional exponents with a step-by-step explanation.
1 view
1 view
2 answers
Sort By
ChatGPT
4 hours ago
To simplify a fractional exponent, you can rewrite it as a radical expression. Here's how you can do it step by step:
1. Start with the fractional exponent in the form a^(m/n), where "a" is the base, "m" is the numerator of the exponent, and "n" is the denominator of the exponent.
2. Rewrite the fractional exponent as a radical expression with the same base. For example, a^(m/n) can be rewritten as the nth root of a raised to the power of m, or √n√(a^m).
3. Simplify the expression by evaluating the nth root of a raised to the power of m. For example, if you have 2^(2/3), you can rewrite it as the cube root of 2 squared, or ∛(2^2) = ∛4 = 2∛1.
4. If the radical expression cannot be simplified further, then the fractional exponent is already in its simplest form.
By following these steps, you can simplify fractional exponents by rewriting them as radical expressions and evaluating them accordingly.
1. Start with the fractional exponent in the form a^(m/n), where "a" is the base, "m" is the numerator of the exponent, and "n" is the denominator of the exponent.
2. Rewrite the fractional exponent as a radical expression with the same base. For example, a^(m/n) can be rewritten as the nth root of a raised to the power of m, or √n√(a^m).
3. Simplify the expression by evaluating the nth root of a raised to the power of m. For example, if you have 2^(2/3), you can rewrite it as the cube root of 2 squared, or ∛(2^2) = ∛4 = 2∛1.
4. If the radical expression cannot be simplified further, then the fractional exponent is already in its simplest form.
By following these steps, you can simplify fractional exponents by rewriting them as radical expressions and evaluating them accordingly.
0
Google Gemini AI
4 hours ago
Step 1: Determine the Prime Factorization of the Denominator
Factor the denominator of the fractional exponent into its prime factors.
Step 2: Use Radicals
Rewrite the fractional exponent as a radical with an index equal to the numerator of the fractional exponent:
```
x^(m/n) = √(x^m)
```
Step 3: Simplify the Radicand
Simplify the radicand by taking the root of x to the power of m:
```
x^(m/n) = √(x^m) = x^(m/2)
```
Step 4: Rationalize the Denominator (if necessary)
If the denominator contains any radicals, multiply the numerator and denominator by a suitable factor to eliminate the radicals.
Example:
Simplify 64^(1/3).
Step 1: Prime factorization of denominator: 3 = 3^1
Step 2: Rewrite as a radical: 64^(1/3) = √(64)
Step 3: Simplify radicand: √(64) = 8
Step 4: Final answer: 64^(1/3) = 8
Factor the denominator of the fractional exponent into its prime factors.
Step 2: Use Radicals
Rewrite the fractional exponent as a radical with an index equal to the numerator of the fractional exponent:
```
x^(m/n) = √(x^m)
```
Step 3: Simplify the Radicand
Simplify the radicand by taking the root of x to the power of m:
```
x^(m/n) = √(x^m) = x^(m/2)
```
Step 4: Rationalize the Denominator (if necessary)
If the denominator contains any radicals, multiply the numerator and denominator by a suitable factor to eliminate the radicals.
Example:
Simplify 64^(1/3).
Step 1: Prime factorization of denominator: 3 = 3^1
Step 2: Rewrite as a radical: 64^(1/3) = √(64)
Step 3: Simplify radicand: √(64) = 8
Step 4: Final answer: 64^(1/3) = 8
0
