1. x^16/x^3
x^16/3
x^48
x^19
x^13**
2. 4^4 • 4^6
4^2
4^6**
4^10
4^24
3. 4^4 • 4^44
4^176
4^48
4^40**
4^28
4. 3^4/3^4 Write the value of the expression.
3
0
1
4**
5. 3^3/3^6
1/27**
1/9
9
-27
1) yes
2)4^4 * 4^6 = 4^(4+6) = 4^10
3)4^(4+44) = 4^48
4) 3^(4-4) = 3^0 = 1
note ANYTHING^0 = 1
5) 3^-3 = 1/3^3 = 1/27 yes
Thanks Damon! :)
You are welcome :)
1. The expression x^16/x^3 can be simplified by subtracting the exponents since we are dividing the same base (x). So, x^16/x^3 = x^(16-3) = x^13.
2. To simplify 4^4 • 4^6, we add the exponents since we are multiplying the same base (4). So, 4^4 • 4^6 = 4^(4+6) = 4^10.
3. Similarly, to simplify 4^4 • 4^44, we add the exponents: 4^(4+44) = 4^48.
4. When dividing two exponents with the same base, we subtract the exponents. So, 3^4/3^4 = 3^(4-4) = 3^0 = 1.
5. In this case, 3^3/3^6, we subtract the exponents since we are dividing the same base (3). Thus, 3^3/3^6 = 3^(3-6) = 3^(-3).
Since any non-zero number raised to a negative power is equal to 1 divided by that same number raised to the positive power, we can rewrite it as 1/3^3 = 1/27.