I need help with the following:
What is the simplified form of 3a^4b^-2c^3? (1 point)
What is –a^-2 if a=-5? (1 point)
What is the simplified form of –(14x)^0y^-7z? (1 point)
What is (-m)^-3n if m=2 and n=-24? (1 point)
3 a^4 c^3 / b^2
-1/(-5)^2 = -1/25
-1 z / y^7
-3n = -3(-24) = +72
(-2)^72 = 2^72 because even power = 4.7*10^21
very big number
ANYTHING AT ALL^0 = 1
Yes, I know that anything with an exponent of 0 =1, but they didn't give me multiple choice questions, which is why I need help..
Thank you Damon~!
You are welcome
To find the simplified form of expressions involving variables and exponents, follow these steps:
1. Apply the exponent rules:
- For the product of variables with the same base, add the exponents.
- For the division of variables with the same base, subtract the exponents.
- For a variable raised to a negative exponent, move it to the denominator and change the sign of the exponent.
- For a variable raised to a power of 0, it becomes 1.
Let's go through each question:
1. What is the simplified form of 3a^4b^-2c^3?
To simplify this expression, we apply the exponent rules:
- The variable 'a' has an exponent of 4.
- The variable 'b' has a negative exponent of -2, so it is moved to the denominator and becomes b^2.
- The variable 'c' has an exponent of 3.
Therefore, the simplified form of 3a^4b^-2c^3 is 3a^4 / b^2c^3.
2. What is –a^-2 if a=-5?
To evaluate this expression, substitute 'a' with its given value (-5):
- Substitute 'a' with -5 in -a^-2: -(-5)^-2.
- Apply the exponent rule: the base (-5) will be squared.
So, -a^-2 = -(-5)^-2 = -(1/(-5)^2) = -(1/25) = -0.04.
3. What is the simplified form of –(14x)^0y^-7z?
To simplify this expression, we apply the exponent rules:
- Any number (except 0) raised to the power of 0 is equal to 1. So, (14x)^0 becomes 1.
- The variable 'y' has a negative exponent of -7, so it is moved to the denominator and becomes y^7.
- The variable 'z' has an exponent of 1 since it is not explicitly mentioned.
Therefore, the simplified form of –(14x)^0y^-7z is -y^7z.
4. What is (-m)^-3n if m=2 and n=-24?
To evaluate this expression, substitute 'm' with 2 and 'n' with -24:
- Substitute 'm' with 2 and 'n' with -24 in (-m)^-3n: -(2)^(-3(-24)).
- Simplify the exponent: -2^72.
Please note that (-2)^72 is a very large number and might not be easily calculated.
Therefore, (-m)^-3n = -2^72 (which is a very large number).