Answer:To simplify the expression (-3/4^3) * (5/2^3) * (2/3^5) using the laws of exponents, you can calculate each part separately and then multiply the results:
(-3/4^3): First, simplify the negative exponent and calculate 4^3.
(-3/4^3) = (-3/64)
(5/2^3): Calculate 2^3.
(5/2^3) = (5/8)
(2/3^5): Calculate 3^5.
(2/3^5) = (2/243)
Now, you can multiply these simplified fractions together:
(-3/64) * (5/8) * (2/243)
To multiply fractions, you simply multiply the numerators together and the denominators together:
(-3 * 5 * 2) / (64 * 8 * 243)
Now, calculate the products in the numerator and denominator:
Numerator: -3 * 5 * 2 = -30
Denominator: 64 * 8 * 243 = 124416
So, the simplified expression is:
-30/124416
You can simplify this fraction further by finding the greatest common divisor (GCD) of the numerator and denominator, but it's already in its simplest form
Answers & Comments
Answer:To simplify the expression (-3/4^3) * (5/2^3) * (2/3^5) using the laws of exponents, you can calculate each part separately and then multiply the results:
(-3/4^3): First, simplify the negative exponent and calculate 4^3.
(-3/4^3) = (-3/64)
(5/2^3): Calculate 2^3.
(5/2^3) = (5/8)
(2/3^5): Calculate 3^5.
(2/3^5) = (2/243)
Now, you can multiply these simplified fractions together:
(-3/64) * (5/8) * (2/243)
To multiply fractions, you simply multiply the numerators together and the denominators together:
(-3 * 5 * 2) / (64 * 8 * 243)
Now, calculate the products in the numerator and denominator:
Numerator: -3 * 5 * 2 = -30
Denominator: 64 * 8 * 243 = 124416
So, the simplified expression is:
-30/124416
You can simplify this fraction further by finding the greatest common divisor (GCD) of the numerator and denominator, but it's already in its simplest form
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