Questions: Simplify. [ (4 x^-3 y^4)^-5(4 x^-3 y^4)^5 ]

Transcript text: Simplify. \[ \left(4 x^{-3} y^{4}\right)^{-5}\left(4 x^{-3} y^{4}\right)^{5} \]

Solution

Solution

Given the expression to simplify is: \[\left(4 x^{-3} y^{4}\right)^{-5}\]

Step 1: Raise the coefficient \(a\) to the power of \(p\)

We calculate \(a^p = 4^{-5} = 0.000977\).

Step 2: Multiply the exponents \(m\) and \(n\) by \(p\)

The new exponents for \(x\) and \(y\) are \(mp = -3 \times -5 = 15\) and \(np = 4 \times -5 = -20\), respectively.

The simplified form of the expression is: \[0.000977 x^{15} y^{-20}\]

Solution

Given the expression to simplify is: \[\left(4 x^{-3} y^{4}\right)^{5}\]

Step 1: Raise the coefficient \(a\) to the power of \(p\)

We calculate \(a^p = 4^{5} = 1024\).

Step 2: Multiply the exponents \(m\) and \(n\) by \(p\)

The new exponents for \(x\) and \(y\) are \(mp = -3 \times 5 = -15\) and \(np = 4 \times 5 = 20\), respectively.

Final Answer:

The simplified form of the expression is: \[1024 x^{-15} y^{20}\]

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