I am not understanding these kinds of problems: I cannot simplify with understanding.
7 times the 4th root of m^3 plus 9 times the 4th root of 256m^3.
it can also be written as:
7 x [m^(3/4)] + 9[256m^(3/4)]
solve it
a correction is in order, as it should be
7 x [m^(3/4)] + 9[(256m^3)^(1/4)]
= 7∜m^3 + 9(∜256∜m^3)
= 7∜m^3 + 9(4∜m^3)
= 43∜m^3
To simplify the expression 7 times the 4th root of m^3 plus 9 times the 4th root of 256m^3, we need to apply the properties of radicals.
Step 1: Simplify the radicands (values inside the radical sign).
The 4th root of m^3 can be written as (m^3)^(1/4). Since the exponent inside the parentheses is already a multiple of 4, we can simplify it to m^(3/4).
Similarly, the 4th root of 256m^3 can be simplified as (256m^3)^(1/4). Simplifying further, we have (4^4 * m^3)^(1/4). Applying the power rule of exponents, this becomes 4^(4 * 1/4) * m^(3 * 1/4), which simplifies to 4m^(3/4).
Step 2: Apply the distributive property of multiplication over addition.
Now that we have simplified the radicands, we can rewrite the expression as:
7 * m^(3/4) + 9 * 4m^(3/4)
Step 3: Combine like terms.
Since both terms have the same exponent (3/4) and a common factor of m, we can combine them:
7m^(3/4) + 36m^(3/4)
Step 4: Simplify further, if possible.
To simplify, we add the coefficients together:
(7 + 36) * m^(3/4)
Which simplifies to:
43 * m^(3/4)
So, the simplified expression is 43 times the 4th root of m^3.