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Simplify the following expression to simplest form using only positive exponents.left bracket, 81, x, to the power minus 4 , y, to the power 32 , right bracket, start superscript, minus, start fraction, 3, divided by, 4, end fraction, end superscript(81x −4 y 32 ) − 43​

Question

Simplify the following expression to simplest form using only positive exponents.left bracket, 81, x, to the power minus 4 , y, to the power 32 , right bracket, start superscript, minus, start fraction, 3, divided by, 4, end fraction, end superscript(81x −4 y 32 ) − 43​

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Solution

The expression you provided is (81x^(-4)y^32)^(-3/4). Here are the steps to simplify it:

  1. Distribute the exponent -3/4 to each part inside the parentheses. Remember that when you raise a power to a power, you multiply the exponents.

    This gives us: 81^(-3/4) * x^(-4*-3/4) * y^(32*-3/4)

  2. Simplify the exponents:

    This gives us: 81^(-3/4) * x^3 * y^-24

  3. Convert the negative exponents to positive by taking the reciprocal.

    This gives us: (1/81^(3/4)) * x^3 * (1/y^24)

  4. Simplify 81^(3/4). The fourth root of 81 is 3, and 3 cubed is 27.

    This gives us: (1/27) * x^3 * (1/y^24)

  5. Finally, we can write the expression in a more standard form:

    This gives us: x^3 / (27y^24)

So, the simplified form of the expression (81x^(-4)y^32)^(-3/4) is x^3 / (27y^24).

This problem has been solved

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