Simplifying Algebra with power to a half

In summary, the equation 3b^1/2 x 4b^0 / 6b^1/2 does not simplify to the expected answer of 2/b and there may be an error in the original equation. The expression contains only multiplication and division, so it can be simplified by performing these operations. However, the simplified form of the expression is 2b^-1, which can also be written as 2/b. The speaker suggests rewriting the expression as a horizontal line with terms above and below to help with simplification.
  • #1
Chapman2233
7
0

Homework Statement



3b^1/2 x 4b^0 / 6b^1/2


3. The Attempt at a Solution [/b]

All the solutions i keep getting do not equal the answer which is 2b^-1 = 2/b.

I am not sure what i am supposed to minus from the first side and put on the second side of the equation?
 
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  • #2
Chapman2233 said:
3b^1/2 x 4b^0 / 6b^1/2

I think you've made an error in your equation. What is it supposed to equal?
 
  • #3
it doesn't equal anything
 
  • #4
That is the only question i was given
 
  • #5
Chapman2233 said:
3b^1/2 x 4b^0 / 6b^1/2
...
I am not sure what i am supposed to minus from the first side and put on the second side of the equation?
It's not referred to as an "equation" because it doesn't contain an equals sign. It's an expression.

You won't "minus" anything because there are no terms here that have been "added". Because this expression contains only multiplication and division, you will probably perform only division and multiplication to simplify it.

It does not simplify to the answer you hoped, so maybe you have copied it wrongly?
Can you rewrite this so that it's a long horizontal line with some terms above that line, and some below the line? That might help you see how to simplify it.
3b^1/2 x 4b^0 / 6b^1/2

3√b · 4b° ÷ (6√b) =
 

What is the meaning of "power to a half" in algebra?

In algebra, "power to a half" refers to the square root of a number or variable. It represents the value that when multiplied by itself, results in the original number or variable. For example, the square root of 16 is 4 because 4 multiplied by itself is equal to 16.

How do I simplify expressions with power to a half?

To simplify expressions with power to a half, you can use the rule that states that the square root of a product is equal to the product of the square roots of each factor. For example, the square root of 36x^2 is equal to the square root of 36 times the square root of x^2, which simplifies to 6x.

Can I simplify fractions with power to a half?

Yes, fractions with power to a half can be simplified using the same rule as above. For example, the square root of (9/16) is equal to the square root of 9 divided by the square root of 16, which simplifies to 3/4.

How do I solve equations with power to a half?

To solve equations with power to a half, you can square both sides of the equation. This will eliminate the power to a half and leave you with a simpler equation to solve. However, it is important to check for extraneous solutions, as squaring both sides may introduce new solutions that are not part of the original equation.

Can I simplify expressions with power to a half and other powers?

Yes, expressions with power to a half and other powers can be simplified using the same rule as above. First, simplify the powers separately, and then apply the rule for simplifying expressions with multiple powers. For example, the square root of 16x^3 is equal to the square root of 16 times the square root of x^3, which simplifies to 4x^(3/2).

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