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 forgot how to do these.
thanks,
No problem! I'll walk you through each of these problems step by step.
1. Simplify 12^2:
To simplify this exponent, simply multiply 12 by itself. So, 12^2 = 12 * 12 = 144.
Answer in standard form: 144
Answer in exponent form: 12^2 = 144
2. Simplify (2^8) * (2^-3):
To simplify this expression, use the exponent property that states: a^m * a^n = a^(m+n). Apply this property to the two exponents:
(2^8) * (2^-3) = 2^(8 + (-3)) = 2^5.
Answer in standard form: 32
Answer in exponent form: 2^5 = 32
3. Simplify 2^15 / 2^8:
To simplify this expression, use the exponent property that states: a^m / a^n = a^(m-n). Apply this property to the two exponents:
2^15 / 2^8 = 2^(15 - 8) = 2^7.
Answer in standard form: 128
Answer in exponent form: 2^7 = 128
4. Simplify 4^5 + 4^2:
To simplify this expression, simply calculate each exponent separately:
4^5 = 4 * 4 * 4 * 4 * 4 = 1024
4^2 = 4 * 4 = 16
Then, add the results together: 1024 + 16 = 1040.
Answer in standard form: 1040
Answer in exponent form: Not applicable, as it cannot be represented as a single exponent expression.
5. Simplify (3^-3)^2:
To simplify this expression, cubed the base inside the parentheses, and then square the result:
(3^-3)^2 = (1/3^3)^2 = (1/27)^2 = 1/729.
Answer in standard form: 1/729
Answer in exponent form: (3^-3)^2 = 1/729
6. Simplify ((2^4) * (2^5)) / (2^6):
To simplify this expression, use the exponent property that states: (a^m * a^n) / a^p = a^(m+n-p). Apply this property to the exponents:
((2^4) * (2^5)) / (2^6) = 2^(4 + 5 - 6) = 2^3.
Answer in standard form: 8
Answer in exponent form: 2^3 = 8
7. Simplify 4^2 - 2^3:
To simplify this expression, calculate each exponent separately:
4^2 = 4 * 4 = 16
2^3 = 2 * 2 * 2 = 8
Then, subtract the second result from the first: 16 - 8 = 8.
Answer in standard form: 8
Answer in exponent form: Not applicable, as it cannot be represented as a single exponent expression.
I hope these explanations helped you understand how to simplify each exponent! Let me know if you have any further questions.