Simplify each exponent. 'Write the answer in standard form and exponent form.
12^2
(2^8)*(2^-3)
2^15/2^8
4^5+4^2
(3^-3)^2
((2)^4*(2)^5)/(2)^6
4^2-2^3
help....i forget how to do these.
thanks,
No problem! I'll walk you through each one step by step.
1. Simplify 12^2:
To simplify an exponent, you just multiply the base by itself the number of times indicated by the exponent.
12^2 means multiplying 12 by itself.
12 * 12 = 144
So, the answer in standard form is 144, and in exponent form, it is 12^2.
2. Simplify (2^8)*(2^-3):
When multiplying exponents with the same base, you add the exponents.
2^8 * 2^-3 = 2^(8 + -3)
Now, simplify the exponent.
2^(8 - 3) = 2^5
So, the answer in standard form is 32, and in exponent form, it is 2^5.
3. Simplify 2^15/2^8:
When dividing exponents with the same base, you subtract the exponents.
2^15 / 2^8 = 2^(15 - 8)
2^7
So, the answer in standard form is 128, and in exponent form, it is 2^7.
4. Simplify 4^5 + 4^2:
To calculate this, you just evaluate each exponent separately, then add the results.
4^5 = 1024
4^2 = 16
Now, add the two results together.
1024 + 16 = 1040
So, the answer in standard form is 1040, and in exponent form, it is 4^5 + 4^2.
5. Simplify (3^-3)^2:
To raise an exponent to another exponent, you multiply the exponents.
(3^-3)^2 = 3^(-3*2)
3^(-6)
So, the answer in standard form is 1/729, and in exponent form, it is 3^(-6).
6. Simplify ((2)^4*(2)^5)/(2)^6:
When multiplying or dividing exponents with the same base, you add or subtract the exponents accordingly.
((2)^4*(2)^5)/(2)^6 = (2^(4 + 5))/(2)^6
2^(9 - 6)
2^3
So, the answer in standard form is 8, and in exponent form, it is 2^3.
7. Simplify 4^2 - 2^3:
Just like in the previous example, evaluate each exponent separately, then subtract the results.
4^2 = 16
2^3 = 8
Now, subtract the two results.
16 - 8 = 8
So, the answer in standard form is 8, and in exponent form, it is 4^2 - 2^3.
I hope this helps! Let me know if you have any further questions.