Final answer:
The equivalent expression for 5^√(m+2)^3, assuming a multiplication between 5 and the cube of the square root of (m+2), would be 5 * (m+2)^(3/2). The expression combines exponential and radical expressions using exponent multiplication rules.
Step-by-step explanation:
The question is asking to identify the equivalent expression for the given expression 5^√(m+2)^3. To find an equivalent expression, we need to use the properties of exponents and roots. Let's first consider a related basic concept:
- When you have an exponent raised to an exponent, you multiply the exponents. For example, (a^b)^c = a^(b*c).
- The cube of a number, or raising a number to the power of 3, is denoted as a^3. To cube an expression with an exponent, you multiply the exponent by 3, according to the rules of cubing exponentials.
- A square root can be expressed as a fractional power where the square root of x is x^(1/2).
Following these rules, let's manipulate the expression:
√(m+2)^3 is the same as (m+2)^(3/2) because you are taking the square root (which is the same as raising to the 1/2 power) and then cubing the result (multipling the exponents).
Now, knowing that 5^1 = 5, and if we assume that the original expression was meant to multiply 5 by the square root of (m+2) cubed, the equivalent expression would simply be:
5 * (m+2)^(3/2)
This assumes there might have been a typo in the original expression, as 5^√(m+2)^3 is not conventionally correct mathematical notation.