Please help me simplify this one please:
15sqrt8x^16/5sqrt2x^4
To simplify the expression 15sqrt(8x^16) / 5sqrt(2x^4), you can follow these steps:
Step 1: Simplify the square roots separately.
- The square root of 8 can be simplified as sqrt(8) = sqrt(4 x 2) = 2sqrt(2).
- The square root of x^16 can be simplified as sqrt(x^16) = x^8.
- The square root of 2 can be kept as is, sqrt(2).
Step 2: Simplify the expression further.
- Now, we have 15 * 2sqrt(2) * x^8 / 5 * sqrt(2) * x^4.
Step 3: Cancel out common factors.
- Cancel out 5 and 15: 15 / 5 = 3.
- Cancel out sqrt(2) and sqrt(2): sqrt(2) / sqrt(2) = 1.
- Cancel out x^4 and x^8: x^8 / x^4 = x^(8-4) = x^4.
Step 4: Simplify the remaining expression.
- After canceling out common factors, the simplified expression is 3 * 2 * x^4.
- This simplifies to 6x^4.
Therefore, the simplified expression is 6x^4.