Simp1ify the following.
2a*a
ab*7a
7pq*3p
3b²*2cd
20m¹²*2m³
2a²
7ab²
21p²q
6b²cd
40m¹⁵
4*3g
7*3h
4d*6
3z*5
6*5r
12g
21h
24d
15z
30r
5t*7
4*3u
7*6p
7gy*3
2*11ht
35t
12u
42p
21gy
22ht
To simplify the expressions, we can follow the rules of exponentiation:
1. 2a * a = 2a^2
2. ab * 7a = 7ab^2
3. 7pq * 3p = 21p^2q
4. 3b² * 2cd = 6b²cd
5. 20m¹² * 2m³ = 40m¹⁵
To simplify the following expressions, you need to perform the indicated operations and simplify any like terms. Here's how you can do it:
1. Simplify 2a * a:
To multiply variables with the same base, you add their exponents. In this case, both "a" have an exponent of 1.
So, 2a * a = 2 * a^1 * a^1 = 2 * a^(1+1) = 2 * a^2 = 2a^2
2. Simplify ab * 7a:
When multiplying variables with different bases but the same exponent, you multiply their coefficients and combine the variables.
So, ab * 7a = (a * a) * (b * 7) = a^1 * a^1 * b * 7 = a^(1+1) * b * 7 = a^2 * b * 7 = 7a^2b
3. Simplify 7pq * 3p:
Similarly, multiply the coefficients and combine the variables.
So, 7pq * 3p = (7 * 3) * (p * p) * q = 21p^1 * p^1 * q = 21p^(1+1) * q = 21p^2q
4. Simplify 3b² * 2cd:
Multiply the coefficients and combine the variables.
So, 3b² * 2cd = (3 * 2) * (b * b) * (c * d) = 6b^(2+2) * c * d = 6b^4cd
5. Simplify 20m¹² * 2m³:
Do the same steps as above, multiplying the coefficients and combining the variables.
So, 20m¹² * 2m³ = (20 * 2) * (m * m * m * m * m * m * m * m * m * m * m * m) = 40m^(12+3) = 40m^15
Therefore, simplified expressions are:
1. 2a*a = 2a^2
2. ab*7a = 7a^2b
3. 7pq*3p = 21p^2q
4. 3b²*2cd = 6b^4cd
5. 20m¹²*2m³ = 40m^15