How do you simplify #(-5ab^-2c^3)(a^-3bc^-2)(-3a^2bc^4) #?

Question

Kennedy Adams · Accepted Answer

The answer is #15c^5#.

#(-5ab^(-2)c^3)(a^(-3)bc^(-2))(-3a^2bc^4)# Apply the exponent product rule #a^m*a^n=a^(m+n)# . #15a^((1+(-3)+2))b^((-2+1+1))c^((3+(-2)+4))# Simplify. #15a^0b^0c^5# Apply exponent rule #x^0=1# #15xx1xx1xxc^5=# #15c^5#

Hazel Anglin · Answer

undefined To simplify the expression (-5ab^-2c^3)(a^-3bc^-2)(-3a^2bc^4), we can combine like terms by multiplying the coefficients and adding the exponents of the variables with the same base.

First, let's simplify the coefficients: -5 * -3 = 15.

Next, let's simplify the variables:

For 'a':
- The exponent of 'a' in the first term is 1 (from 'a' in the first term and '-3' in the second term).
- The exponent of 'a' in the second term is -3 (from 'a' in the second term).
- The exponent of 'a' in the third term is 2 (from 'a^2' in the third term).
Combining the exponents: 1 + (-3) + 2 = 0. So, 'a^0' simplifies to 1.

For 'b':
- The exponent of 'b' in the first term is -2 (from 'b^-2' in the first term).
- The exponent of 'b' in the second term is -1 (from 'b' in the first term and '-2' in the second term).
- The exponent of 'b' in the third term is 1 (from 'b' in the third term).
Combining the exponents: -2 + (-1) + 1 = -2. So, 'b^-2' remains as 'b^-2'.

For 'c':
- The exponent of 'c' in the first term is 3 (from 'c^3' in the first term).
- The exponent of 'c' in the second term is 0 (since 'c' is not present in the second term).
- The exponent of 'c' in the third term is 4 (from 'c^4' in the third term).
Combining the exponents: 3 + 0 + 4 = 7. So, 'c^7' remains as 'c^7'.

Putting it all together, the simplified expression is: 15b^-2c^7.