simplify the following
7pq
----
14p(to the power2)q(to the power -2)
also
(5ab)All to the power -2 x 15a (to the power 2) x b (to the power 3)
7 pq/[14p^2*q^-2)]
= (1/2)q^3/p
(Exponents in the denominator can be subtracted from exponents in the numerator, or vice versa, if they are exponents of the same number).
1/q-2 = q^2
(5ab)^-2 * 15a^2b^3 =
15 a^2b^3/[25 a^2 b^2]
=(15/25)b = (3/5)b
To simplify the given expressions, we can apply the laws of exponents.
1. Simplifying (7pq) / (14p^2q^-2):
First, let's simplify the numerator:
7pq
Now, let's simplify the denominator:
14p^2q^-2
To divide the terms in the numerator and denominator, we can subtract the exponents of the variables:
7pq / (14p^2 * 1/q^2)
When dividing, dividing by q^-2 is the same as multiplying by q^2, so we can rewrite the expression as:
7pq / (14p^2 * q^2)
Next, we can simplify the coefficients and combine like terms:
7/14 equals 1/2, so the expression becomes:
(1/2)pq / (p^2 * q^2)
Finally, we can simplify the expression by canceling out common factors:
(1/2) * p / (p^2 * q)
2. Simplifying (5ab)^-2 * 15a^2 * b^3:
Let's first simplify the terms that are raised to powers:
(5ab)^-2 can be rewritten as 1 / (5ab)^2. Squaring (5ab) gives us 25a^2b^2.
So, the expression becomes: 1 / 25a^2b^2 * 15a^2 * b^3
Now, we can simplify by multiplying and combining like terms:
Multiplying:
= (1 * 15a^2 * b^3) / (25a^2b^2)
Combining like terms:
= (15a^2b^3) / (25a^2b^2)
Finally, we can cancel out common factors:
= (3/5) * b^3 / b^2
= 3/5 * b (as b^3/b^2 = b^1 = b)
So, the simplified expression is: (3/5) * b.