I have to simplify this:
(y^(1/4)*Z^4)^(-4/5)
My answer:
(2z)^(1/2)/4z^4
Correct?
Simplify (3-2SQRT2)(SQRT6-5)
I have no idea how to foil this one.
I don't think (2z)^(1/2)/4z^4 can be correct, since y has disappeared.
Take it in steps, by distributing th power:
(y^(1/4)*Z^4)^(-4/5) =
(y^(1/4))^(-4/5)(*Z^4)^(-4/5)
Now, what's the rule for raising powers?
As for
(3-2SQRT2)(SQRT6-5)
I don't really get it to be very simple!
All I can do is multiply it out:
3sqrt6-15-2sqrt2sqrt6+10sqrt2
and collect the terms.
It it helps at all, you can note that:
sqrt(12) = sqrt(4)*sqrt(3) = 2sqrt(3)
but that doesn't help much!
To simplify the expression (y^(1/4) * Z^4)^(-4/5), you can follow these steps:
Step 1: Apply the power rule for exponents. When raising a power to a negative exponent, you can rewrite it as the reciprocal of that power raised to the positive exponent. In this case, we have:
(y^(1/4) * Z^4)^(-4/5) = 1 / (y^(1/4))^(-4/5) * (Z^4)^(-4/5)
Step 2: Simplify the exponents in the denominator. Distribute the exponent to both the y and Z terms, which gives us:
1 / y^(-4/20) * Z^(-16/20)
Step 3: Further simplify the exponents. In this case, we can simplify by multiplying both the numerator and denominator by the reciprocal of the exponent, which will change the sign of the exponent:
1 / (1/y^(4/20) * 1/Z^(16/20))
Step 4: Simplify the exponents in the numerator. When you multiply powers with the same base but different exponents, you can add their exponents. In this case, we have:
1 / (1/y^(1/5) * 1/Z^(4/5))
Step 5: Rewrite the expression with positive exponents. Taking the reciprocal of a fraction is the same as flipping the numerator and denominator. Therefore, we have:
y^(1/5) / Z^(4/5)
So, the simplified form of (y^(1/4) * Z^4)^(-4/5) is y^(1/5) / Z^(4/5).
Now, for the second question: Simplify (3 - 2√2)(√6 - 5)
To simplify this expression using the FOIL method, which stands for First, Outer, Inner, Last, follow these steps:
Step 1: Multiply the First terms: 3 * √6 = 3√6
Step 2: Multiply the Outer terms: 3 * (-5) = -15
Step 3: Multiply the Inner terms: (-2√2) * √6 = -2√12
Step 4: Multiply the Last terms: (-2√2) * (-5) = 10√2
Step 5: Combine the like terms resulting from the multiplication:
3√6 - 15 - 2√12 + 10√2
Now, let's simplify the expression further. To do this, we need to simplify the square roots.
Step 6: Simplify the square roots:
The square root of 6 cannot be simplified further since it does not have any perfect square factors.
For the square root of 12, we can break it down into the square root of 4 times the square root of 3. So, the square root of 12 simplifies to 2√3.
Step 7: Plug in the simplified square roots to get the final simplified expression:
3√6 - 15 - 2√12 + 10√2 = 3√6 - 15 - 2(2√3) + 10√2 = 3√6 - 15 - 4√3 + 10√2.
Therefore, the simplified form of (3 - 2√2)(√6 - 5) is 3√6 - 15 - 4√3 + 10√2.