Simplify the expressions
(ab^2c)^-1 / a^8b^2c^-4b^3
(ab^2c)^-1 = a^-1b^-2c^-1
a^8b^2c^-4b^3 = a^8b^5c^-4
a^-1b^-2c^-1 / a^8b^5c^-4 = a^-9b^-7c^3
= c^3 / a^9b^7
ok i get it now.
for this question..
3square root of 1/2x+1 +2=5
the +2=5 is out of the square root.
so do i get rid of the square root first or subtract 2 from 5
do the reverse of PEMDAS
3√1/(2x+1) + 2 = 5
3/√(2x+1) = -3
1/√(2x+1) = -1
1 = -√(2x+1)
squaring yields
1 = 2x+1
0 = 2x
x = 0
check:
3/√1 + 2 = 5
yes
Rather a poor exercise, imho
To simplify the given expression:
(ab^2c)^-1 / a^8b^2c^-4b^3
Step 1: Deal with negative exponents
Recall that a negative exponent in the numerator can be moved to the denominator and become positive, and vice versa. In this case, we can rewrite the expression as:
1 / (ab^2c)
Step 2: Combine like terms
Dividing by a fraction is the same as multiplying by its reciprocal. So, let's invert the denominator and multiply it by the numerator:
1 * (a^8b^2c^-4b^3) / (ab^2c)
Step 3: Simplify the expression using the exponent rules
When multiplying exponents with the same base, you add their exponents. Apply this rule to simplify the expression further:
a^8 * b^(2-2-3) * c^(-4-1)
Step 4: Simplify the exponents
Now we can simplify the exponents:
a^8 * b^(-3) * c^(-5)
Step 5: Combine the variables
Our expression is now:
a^8 * (1 / b^3) * (1 / c^5)
Finally, we can rewrite the expression in a simpler form:
(a^8 / b^3c^5)