Answer:
-27/8575
Step-by-step explanation:
Here,
(3/7)`¹ × (7/3)`⁴ × (-5)`¹ × (1/5)
(7/3) × (3/7)⁴ × (-1/5) × 1/5
7/3 × 81/2401 × -1/25
27/343 × -1/25
To solve the given task, let's break it down step by step, ensuring accuracy at each stage:
Step 1: Simplify the expressions within the parentheses.
(3/7)-¹ x (7/3)-⁴ x (-5)-¹ x (1/5)
To simplify the negative exponents, we can apply the rule:
a⁻ⁿ = 1 / aⁿ
So, the expression becomes:
(7/3)¹ x (3/7)⁴ x (-1/5)¹ x (1/5)
Step 2: Simplify the fractions and exponents.
Using the power property of fractions, we have:
(7¹ / 3¹) x (3⁴ / 7⁴) x (-1¹ / 5¹) x (1¹ / 5¹)
This simplifies to:
7/3 x 3⁴/7⁴ x -1/5 x 1/5
Step 3: Cancel out common terms in the fractions and simplify.
Canceling out common terms:
7/3 x 3⁴/7⁴ = 7/7⁴ (canceling out the 3 and 7)
1/7³ (simplifying 3⁴ as 3³ x 3)
1/7³ x (-1/5) x 1/5
Step 4: Multiply the fractions.
To multiply fractions, multiply the numerators and denominators separately:
(1 x (-1) x 1) / (7³ x 5 x 5)
-1 / (7³ x 5²)
Step 5: Evaluate the final answer.
Using the exponent rule (a^n x a^m = a^(n+m)):
-1 / (7³ x 5²) = -1 / (343 x 25)
Calculating the denominator:
343 x 25 = 8575
So, the final answer is:
-1 / 8575
I hope this helps! :)
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Answers & Comments
Answer:
-27/8575
Step-by-step explanation:
Here,
(3/7)`¹ × (7/3)`⁴ × (-5)`¹ × (1/5)
(7/3) × (3/7)⁴ × (-1/5) × 1/5
7/3 × 81/2401 × -1/25
27/343 × -1/25
-27/8575
To solve the given task, let's break it down step by step, ensuring accuracy at each stage:
Step 1: Simplify the expressions within the parentheses.
(3/7)-¹ x (7/3)-⁴ x (-5)-¹ x (1/5)
To simplify the negative exponents, we can apply the rule:
a⁻ⁿ = 1 / aⁿ
So, the expression becomes:
(7/3)¹ x (3/7)⁴ x (-1/5)¹ x (1/5)
Step 2: Simplify the fractions and exponents.
Using the power property of fractions, we have:
(7¹ / 3¹) x (3⁴ / 7⁴) x (-1¹ / 5¹) x (1¹ / 5¹)
This simplifies to:
7/3 x 3⁴/7⁴ x -1/5 x 1/5
Step 3: Cancel out common terms in the fractions and simplify.
Canceling out common terms:
7/3 x 3⁴/7⁴ = 7/7⁴ (canceling out the 3 and 7)
1/7³ (simplifying 3⁴ as 3³ x 3)
So, the expression becomes:
1/7³ x (-1/5) x 1/5
Step 4: Multiply the fractions.
To multiply fractions, multiply the numerators and denominators separately:
(1 x (-1) x 1) / (7³ x 5 x 5)
This simplifies to:
-1 / (7³ x 5²)
Step 5: Evaluate the final answer.
Using the exponent rule (a^n x a^m = a^(n+m)):
-1 / (7³ x 5²) = -1 / (343 x 25)
Calculating the denominator:
343 x 25 = 8575
So, the final answer is:
-1 / 8575
I hope this helps! :)