Use the appropriate laws of indices to simplify these expressions.Show the working
a) (4x^2×3x^4)/6x^4
We can simplify this expression by using the laws of indices:
a) (4x^2 × 3x^4) / 6x^4
= (12x^6) / (6x^4) (multiply the coefficients and add the powers of x)
= 2x^(6-4)
= 2x^2
Therefore, (4x^2 × 3x^4) / 6x^4 simplifies to 2x^2.
To simplify the expression (4x^2 × 3x^4) / 6x^4 using the laws of indices, we can follow these steps:
Step 1: Combine the numerical coefficients: (4 × 3) = 12.
Step 2: Multiply the variables with the same base by adding their exponents: x^2 × x^4 = x^(2+4) = x^6.
Step 3: Divide the exponents in the denominator from the numerator: x^6 / x^4 = x^(6-4) = x^2.
Step 4: Putting it all together: (4x^2 × 3x^4) / 6x^4 = (12x^6) / (6x^4) = 2x^(6-4) = 2x^2.
So, the simplified expression is 2x^2.