Simplify (5π^β2π^β9)/(7π^β8π^5)^β2
and write your answer without using negative exponents.
(5π^β2π^β9)/(7π^β8π^5)^β2
= ( 5/q^2)(2/d^9) * (7q^-8 d^5)^2
= (5 / (q^2d^9)) * (49q^-16 d^10)
= 245d/q^18
https://www.wolframalpha.com/input/?i=simplify+%285q%5E%E2%88%922d%5E%E2%88%929%29%2F%287q%5E%E2%88%928d%5E5%29%5E%E2%88%922
5π^β2π^β9 = 5 / q^2d^9
7π^β8π^5)^β2 = q^16 /49d^10
now divide and you have
5/q^2d^9 * 49d^10 / q^16 = 245d / q^18
To simplify the expression (5π^β2π^β9)/(7π^β8π^5)^β2 without using negative exponents, we will use the properties of exponents.
Step 1: Distribute the exponent outside of the parentheses.
(5π^β2π^β9)/(7π^β8π^5)^β2 becomes:
(5π^β2π^β9) / (1/(7π^β8π^5)^2)
Step 2: Simplify the expression inside the parentheses by applying the power of a power rule.
(7π^β8π^5)^2 = 7^2 * π^(β8 * 2) * d^(5 * 2) = 49π^β16π^10
Now the expression becomes (5π^β2π^β9) / (1/(49π^β16π^10))
Step 3: Multiply by the reciprocal of the second fraction.
When dividing by a fraction, we can multiply by its reciprocal instead.
So, (5π^β2π^β9) * (49π^16π^10)
Step 4: Apply the power of a product rule to simplify the expression.
Multiplying two exponents with the same base, we add their powers.
So, (5 * 49)π^(β2 + 16)π^(β9 + 10)
Simplifying further, we have:
245π^14π^1
Hence, the simplified expression without using negative exponents is 245π^14π.