Simplify the following expression to simplest form using only positive exponents. (64x^(-2)y^(-10))^((3)/(2)) Answer:

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Simplify the following expression to simplest form using only positive exponents.  (64x^(-2)y^(-10))^((3)/(2)) Answer:

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Understand Expression and Rule: Understand the expression and the exponent rule. The expression is (64x^(-2)y^(-10))^((3)/(2)). We need to apply the power of a power rule, which states that (a^m)^n = a^(m*n). We will apply this rule to each part of the expression separately.Apply Power of Power Rule to Coefficient: Apply the power of a power rule to the numerical coefficient. The numerical coefficient is 64, which is a perfect square (8^2). We raise it to the power of (3/2), which is the same as taking the square root and then cubing the result. (64)^(3/2) = (8^2)^(3/2) = 8^(2*(3/2)) = 8^3 = 512.Apply Power of Power Rule to x Term: Apply the power of a power rule to the x term. The x term is x^(-2). We raise it to the power of (3/2). (x^(-2))^(3/2) = x^((-2)*(3/2)) = x^(-3). To express the exponent as positive, we take the reciprocal of x^3. x^(-3) = 1/x^3.Apply Power of Power Rule to y Term: Apply the power of a power rule to the y term. The y term is y^(-10). We raise it to the power of (3/2). (y^(-10))^(3/2) = y^((-10)*(3/2)) = y^(-15). To express the exponent as positive, we take the reciprocal of y^15. y^(-15) = 1/y^15.Combine Results: Combine the results from Steps 2, 3, and 4. We have 512 for the numerical coefficient, 1/x^3 for the x term, and 1/y^15 for the y term. Combining these, we get: 512 * (1/x^3) * (1/y^15) = 512 / (x^3 * y^15).

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(64 x^{-2} y^{-10}\right)^{\frac{3}{2}}$ $\newline$ Answer:

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Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(64 x^{-2} y^{-10}\right)^{\frac{3}{2}}$ $\newline$ Answer: