this isn't the same question as my last post!! it's the second out of three.
Hello! I'm looking over one of my tests and trying to see how to do things I got wrong, but I'm having trouble with three of the questions. Here's one of them:
Find the simplified form of the equation:
)-2
( 3 )
------
4
( 2b )
my answer was:
( 27 )
------
64
( 8b )
the correct answer is:
( 27 )
------
12
( 8b )
how do I get this answer?
(if you don't understand the formatting of the numbers, here they are in a different format that you may be able to understand better)
question: (3/2b^4)^-2
my answer: (27/8b^64)
real answer: (27/8b^12)
When you have a fraction raised to a negative exponent, flip the fraction and make the exponent positive.
e.g. (4/5)^-3 = (5/4)^3 = 125/64
for yours: (3/2b^4)^-2 -----> now here is a problem, did you mean (3/(2b^4) )^-2 ??
let's assume that's what you meant:
(3/(2b^4) )^-2
= ( 2b^4/3)^2
= 4 b^8 / 9
looking at the given answer, I suspect that the exponent was -3 instead of -2
so (3/(2b^4) )^-3
= (2b^4/3)^3
= 8b^12/27 , does not match your given answer
check your typing of the question,
To find the simplified form of the given equation (3/2b^4)^-2, you need to understand the rules of exponents. The rule you'll use here is the negative exponent rule, which states that any term raised to a negative power can be rewritten by taking the reciprocal of the term and changing the sign of the exponent.
Let's break it down step by step:
Step 1: Start by simplifying the numerator. The numerator is 3, which remains the same.
Step 2: Simplify the denominator. The denominator is (2b^4). Since we have a negative exponent, we need to apply the negative exponent rule. The reciprocal of 2b^4 is 1/(2b^4), and the negative exponent becomes positive. Therefore, the denominator simplifies to 1/(2b^4).
Step 3: Now we have (3) / (1/(2b^4)). Remember that dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite this as (3) * (2b^4) = 6b^4.
Step 4: Since the exponent outside the parentheses is -2, we can apply the negative exponent rule again. The reciprocal of 6b^4 is 1/(6b^4), and the negative exponent becomes positive. Therefore, the simplified form is (1/(6b^4))^2.
Step 5: Squaring a fraction means to multiply it by itself. So (1/(6b^4))^2 equals (1/(6b^4)) * (1/(6b^4)).
Step 6: When multiplying fractions, you multiply the numerators together and the denominators together. So the numerator becomes 1 * 1 = 1, and the denominator becomes (6b^4) * (6b^4) = 36b^8.
Therefore, the simplified form of the equation (3/2b^4)^-2 is 1 / (36b^8).
If you simplify the real answer, (27 / 8b^12), you'll see that it is equivalent to 1 / (36b^8).