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(2x ⋅ -3/y)^-3 ⋅ (-5x/y)^2

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1 vote

Answer:

(-30x^2/y^2)^5

Explanation:

First, we can simplify the exponent in the first term by using the property that (a^m)^n = a^(m⋅n). This property tells us that we can calculate the exponent of the first term by multiplying the exponent of the base by the exponent of the power, which gives us (-3)⋅(-3) = 9. This means that the first term can be rewritten as (2x ⋅ -3/y)^9.

Next, we can simplify the second term by calculating its exponent in the same way, which gives us (-2)⋅(2) = -4. This means that the second term can be rewritten as (-5x/y)^-4.

We can then combine the two terms by using the property that (a^m)⋅(b^n) = (a⋅b)^(m+n). This property tells us that we can calculate the exponent of the combined terms by adding the exponents of the individual terms, which gives us 9 + (-4) = 5. This means that the entire expression can be rewritten as (2x ⋅ -3/y)^9 ⋅ (-5x/y)^-4 = (2x⋅-3/y⋅-5x/y)^5.

Finally, we can simplify the base of the combined terms by multiplying the factors together, which gives us (2x⋅-3/y⋅-5x/y) = -30x^2/y^2. This means that the entire expression can be rewritten as (-30x^2/y^2)^5.

User Harman
by
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5 votes

Answer: -25y/216x

Step-by-step explanation: - 25y / 216x

User Bun Suwanparsert
by
8.0k points

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