I have to find the exact value(so in fraction form.. like 1231231/41231 or something) of a^4b^2/c^2 , a = (2/5)^2, b = (8/5)^5 c= (4/5)^10 I'm honestly not sure how to get around to doing it with working
LCD: 3 * 4 * 11 * 7 = 924
so...
2/3 = 2(308)/924 = 616/924
3/4 = 3(231)/924 = 693/924
2/11 = 2(84)/924 = 168/924
5/21 = 5(44)/924 = 220/924
if you can't get the answer from those, then go to your teacher for help...immediately !!
one problem at a time.
@ƒ
[307/308]
a^4b^2/c^2 , a = (2/5)^2, b = (8/5)^5 c= (4/5)^10
a^4 = (2/5)^8 = 2^8/5^8
b^2 = (8/5)^10 = 2^30/5^10
c^2 = (4/5)^20 = 2^40/5^20
a^2b/c = 2^(8+30-40)/5^(8+10-20) = 2^-2/5^-2 = 5^2/2^2 = 25/4
To find the exact value of the expression (a^4b^2)/c^2, where a = (2/5)^2, b = (8/5)^5, and c = (4/5)^10, you need to perform a series of calculations. Here's a step-by-step guide:
Step 1: Substitute the values of a, b, and c into the expression.
(a^4b^2)/c^2 = [(2/5)^2^4 * (8/5)^5^2] / [(4/5)^10^2]
Step 2: Simplify the exponents first.
(a^4b^2)/c^2 = [(2/5)^8 * (8/5)^10] / [(4/5)^20]
Step 3: Calculate the powers using the properties of exponents.
(a^4b^2)/c^2 = [(2^8 / 5^8) * (8^10 / 5^10)] / [4^20 / 5^20]
Step 4: Simplify the fractions separately.
(a^4b^2)/c^2 = [2^8 * 8^10] / [4^20 * 5^8]
Step 5: Calculate the powers of 2, 4, and 8.
(a^4b^2)/c^2 = [256 * 1073741824] / [1099511627776 * 390625]
Step 6: Simplify the numerator and denominator separately.
(a^4b^2)/c^2 = (274877906944) / (428750964712448)
Therefore, the exact value of the expression (a^4b^2)/c^2 is 274877906944/428750964712448, which cannot be reduced any further.