Question

Simplify (5𝑞^−2𝑑^−9)/(7𝑞^−8𝑑^5)^−2

and write your answer without using negative exponents.

Answer 1

(5𝑞^−2𝑑^−9)/(7𝑞^−8𝑑^5)^−2

= ( 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

Answer 2

5𝑞^−2𝑑^−9 = 5 / q^2d^9

7𝑞^−8𝑑^5)^−2 = q^16 /49d^10
now divide and you have

5/q^2d^9 * 49d^10 / q^16 = 245d / q^18

Answer 3

[AI-generated answer — Explain Bot]

To simplify the expression (5𝑞^−2𝑑^−9)/(7𝑞^−8𝑑^5)^−2 without using negative exponents, we will use the properties of exponents.

Step 1: Distribute the exponent outside of the parentheses.
(5𝑞^−2𝑑^−9)/(7𝑞^−8𝑑^5)^−2 becomes:
(5𝑞^−2𝑑^−9) / (1/(7𝑞^−8𝑑^5)^2)

Step 2: Simplify the expression inside the parentheses by applying the power of a power rule.
(7𝑞^−8𝑑^5)^2 = 7^2 * 𝑞^(−8 * 2) * d^(5 * 2) = 49𝑞^−16𝑑^10

Now the expression becomes (5𝑞^−2𝑑^−9) / (1/(49𝑞^−16𝑑^10))

Step 3: Multiply by the reciprocal of the second fraction.
When dividing by a fraction, we can multiply by its reciprocal instead.
So, (5𝑞^−2𝑑^−9) * (49𝑞^16𝑑^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)𝑞^(−2 + 16)𝑑^(−9 + 10)

Simplifying further, we have:
245𝑞^14𝑑^1

Hence, the simplified expression without using negative exponents is 245𝑞^14𝑑.