Here are the questions I need help with, please help.
[(1/4)^-3 divide sign (1/4)^2]^-2
I got (1/4)^10 but I got it wrong
(3^1/2)^3
_______ I got 1/216
9
(-56r^2)divide sign (-7r^2)= I got 8r
x(y)(x)(2y)
(12) (10xy^3) (3x^2y^2) (5x) (2y)
simplify sqaure root of 160000
simplify sqaure root of 0.04
simplify 3 * square root 81
simplify square root of 900
simplify square root of 0.0025simplify [(a^2bc^4)(ab^3c^2)]^2
___________________
(b^2c^5)^3
what is 4^-5/2 expressed as a radical with positive exponents
Thank you so much
[(1/4)^-3 ÷ (1/4)^2]^-2
inside the square brackets we are dividing powers with the same base, so keep the base and subtract the exponents
= [ (1/4)^(-3 -2) ]^2
= [(1/4)^-5]^2
= (1/4)^-10
= 4^10
(3^1/2)^3
_______
9
= 3^(3/2) / 3^2
= 3^(3/2-2)
= 3^(-1/2) = 1/3^(1/2) or 1/√3
(-56r^2) ÷ (-7r^2)
= (-56r^2)/(-7r^2)
= 8
How did you get 8r, there is an r^2 on top and r^2 at the bottom so they divide out to get 1
For the rest of the questions, I can't tell where one ends and the next one begins
for all the questions beginning with "simplify", did you not notice that in each case you are taking the square root of a perfect square ?
e.g.
simplify 3√81 = 3(9) = 27
etc
I'd be happy to help you with your questions. Let's go through each one step by step:
1. To simplify [(1/4)^-3 ÷ (1/4)^2]^-2:
- Start by simplifying the expression inside the square brackets: (1/4)^-3 ÷ (1/4)^2 = (4^3)/(4^2) = 4^3-2 = 4^1 = 4.
- Now, raise the result (4) to the power of -2: 4^-2 = 1/(4^2) = 1/16.
2. To simplify (3^(1/2))^3 ÷ 9:
- First, simplify the expression inside the parentheses: 3^(1/2) = √3.
- Cube the result: (√3)^3 = √3 × √3 × √3 = 3√3.
- Divide 3√3 by 9: (3√3)/9 = √3/3 = (1/3)√3.
3. To solve (-56r^2) ÷ (-7r^2):
- Divide the numbers first: (-56) ÷ (-7) = 8.
- Divide the variables with the same exponent: r^2 ÷ r^2 = 1.
- Therefore, the result is 8.
4. To simplify x(y)(x)(2y):
- Multiply the variables together: x × y × x × 2y = 2x^2y^2.
5. To simplify (12)(10xy^3)(3x^2y^2)(5x)(2y):
- Multiply all the numbers together: 12 × 10 × 3 × 5 × 2 = 3600.
- Multiply all the x-variables together: x × x × x^2 × x = x^4.
- Multiply all the y-variables together: y^3 × y^2 × y × y = y^8.
- Therefore, the simplified expression is 3600x^4y^8.
6. To simplify the square root of 160000:
- Notice that 160000 is a perfect square of 400.
- Therefore, √160000 = √(400 × 400) = 400.
7. To simplify the square root of 0.04:
- Write 0.04 as a fraction: 0.04 = 4/100 = 1/25.
- Take the square root of 1/25: √(1/25) = 1/√25 = 1/5.
8. To simplify 3 * square root of 81:
- Take the square root of 81: √81 = 9.
- Multiply 3 by 9: 3 × 9 = 27.
9. To simplify the square root of 900:
- Notice that 900 is a perfect square of 30.
- Therefore, √900 = √(30 × 30) = 30.
10. To simplify the square root of 0.0025:
- Write 0.0025 as a fraction: 0.0025 = 25/10000 = 1/100 × 1/100 = (1/100)^2.
- Take the square root of (1/100)^2: √((1/100)^2) = 1/100.
11. To simplify [(a^2bc^4)(ab^3c^2)]^2 ÷ (b^2c^5)^3:
- Simplify the numerator first: (a^2bc^4)(ab^3c^2) = a^3b^4c^6.
- Simplify the denominator: (b^2c^5)^3 = b^6c^15.
- Divide the numerator by the denominator: (a^3b^4c^6) ÷ (b^6c^15) = a^3b^(-2)c^(-9).
12. To express 4^(-5/2) as a radical with positive exponents:
- Rewrite 4 as 2^2: 4^(-5/2) = (2^2)^(-5/2) = 2^(-10/2).
- Simplify the exponent: 2^(-10/2) = 2^(-5).
- Rewrite with a positive exponent and inside a radical: 2^(-5) = 1/√(2^5) = 1/√32.