Write (9m) ^4 without exponents.
The Correct Answer and Explanation is:
To write ((9m)^4) without exponents, we need to expand it by multiplying ((9m)) by itself four times. This process is based on the definition of exponents, which means repeated multiplication.
So, ((9m)^4) is equivalent to:
[
(9m) \times (9m) \times (9m) \times (9m)
]
Step 1: Expand the expression
Each term in the product involves multiplying (9) by (m), and we do this four times. This can be broken down into two parts:
- The coefficient: (9 \times 9 \times 9 \times 9)
- The variable (m): (m \times m \times m \times m)
Step 2: Simplify the numbers
We can simplify the coefficient (9 \times 9 \times 9 \times 9) step by step:
[
9 \times 9 = 81
]
[
81 \times 9 = 729
]
[
729 \times 9 = 6561
]
Thus, (9 \times 9 \times 9 \times 9 = 6561).
Step 3: Simplify the variables
The variable part (m \times m \times m \times m) is the same as (m^4), based on the exponent rule where multiplying a variable with the same base adds the exponents. So:
[
m \times m \times m \times m = m^4
]
Step 4: Combine the results
Now, we combine the simplified coefficient (6561) with the variable part (m^4):
[
(9m)^4 = 6561m^4
]
Conclusion:
The expression ((9m)^4) without exponents is:
[
6561m^4
]
This expanded form shows the result of multiplying (9m) by itself four times. By following the basic exponent rules of multiplying numbers and variables, we arrived at this simplified version. The process involves careful handling of both the numerical coefficient and the variable part separately.