How to simplify?
(√3)/(√f^-3)
Taking it just the way you typed it ...
= √3/( (√f)^-3)
= √( 3/f^-3)
= √(3f^3)
= f√(3f)
How did √(3f^3) become f√(3f)? That's the part I'm confused about.
√(3f^3)
= √3 * √(f^2) * √f
= √3*f*√f
= f√3√f
= f√(3f)
Thanks! I get it completely now :).
To simplify the expression (√3)/(√f^-3), we can follow a few steps:
Step 1: Simplify the exponents:
- The denominator has an exponent of -3. We can simplify this by moving it to the numerator and changing the exponent sign:
(√3)/(√(1/f^3))
Step 2: Simplify the square roots:
- The square root in the numerator can be simplified since the square root of 3 is not a perfect square. We multiply the fraction by the square root of the denominator in order to rationalize the denominator:
((√3)/(√(1/f^3))) * ((√f^3)/(√f^3))
Step 3: Simplify the numerator:
- Multiply the terms in the numerator:
(√3 * √f^3)/(√(1/f^3))
Step 4: Simplify the denominator:
- Multiply the terms in the denominator:
(√3 * √f^3)/(√1 * √(1/f^3))
Step 5: Simplify the square roots further:
- The square root of f^3 is equal to f^(3/2) since the sqrt(f^3) = sqrt(f^2 * f) = f^(3/2):
(√3 * f^(3/2))/(√1 * √(1/f^3))
Step 6: Simplify the square root of 1 and the reciprocal:
- The square root of 1 is simply 1, and the square root of (1/f^3) is 1/f^(3/2):
(√3 * f^(3/2))/(1 * 1/f^(3/2))
Step 7: Simplify further:
- We can divide f^(3/2) in the numerator and denominator:
(√3 * f^(3/2))/(1/f^(3/2)) = (√3 * f^(3/2)) * (f^(3/2)/1)
Step 8: Simplify the exponents in the denominator:
- When multiplying with the same base, we add the exponents:
(√3 * f^(3/2)) * (f^(3/2)/1) = (√3 * f^(3/2)) * f^(3/2)
Step 9: Simplify the multiplication in the numerator:
- When multiplying with the same base, we add the exponents:
(√3 * f^(3/2)) * f^(3/2) = √3 * f^(3/2 + 3/2)
Step 10: Simplify the exponents in the numerator:
(√3 * f^(3/2 + 3/2)) = √3 * f^3
Therefore, the simplified form of the expression (√3)/(√f^-3) is √3 * f^3.