Solve 4xy^2/9zadiv(3z^4a/2x^2y)^-2

$$\frac { 4 x y ^ { 2 } } { 9 z a } \div ( \frac { 3 z ^ { 4 } a } { 2 x ^ { 2 } y } ) ^ { - 2 }$$

Evaluate

$$\frac{az^{7}}{x^{3}}$$

Solution Steps

To raise \frac{3z^{4}a}{2x^{2}y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{4xy^{2}}{9za}}{\frac{\left(3z^{4}a\right)^{-2}}{\left(2x^{2}y\right)^{-2}}}$$

Divide \frac{4xy^{2}}{9za} by \frac{\left(3z^{4}a\right)^{-2}}{\left(2x^{2}y\right)^{-2}} by multiplying \frac{4xy^{2}}{9za} by the reciprocal of \frac{\left(3z^{4}a\right)^{-2}}{\left(2x^{2}y\right)^{-2}}.

$$\frac{4xy^{2}\times \left(2x^{2}y\right)^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Expand \left(2x^{2}y\right)^{-2}.

$$\frac{4xy^{2}\times 2^{-2}\left(x^{2}\right)^{-2}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{4xy^{2}\times 2^{-2}x^{-4}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{4xy^{2}\times \frac{1}{4}x^{-4}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Multiply 4 and \frac{1}{4} to get 1.

$$\frac{xy^{2}x^{-4}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$\frac{x^{-3}y^{2}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Multiply y^{2} and y^{-2} to get 1.

$$\frac{x^{-3}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Expand \left(3z^{4}a\right)^{-2}.

$$\frac{x^{-3}}{9za\times 3^{-2}\left(z^{4}\right)^{-2}a^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{x^{-3}}{9za\times 3^{-2}z^{-8}a^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{x^{-3}}{9za\times \frac{1}{9}z^{-8}a^{-2}}$$

Multiply 9 and \frac{1}{9} to get 1.

$$\frac{x^{-3}}{zaz^{-8}a^{-2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -8 to get -7.

$$\frac{x^{-3}}{z^{-7}aa^{-2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{x^{-3}}{z^{-7}a^{-1}}$$

Expand

$$\frac{az^{7}}{x^{3}}$$

Solution Steps

To raise \frac{3z^{4}a}{2x^{2}y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{4xy^{2}}{9za}}{\frac{\left(3z^{4}a\right)^{-2}}{\left(2x^{2}y\right)^{-2}}}$$

Divide \frac{4xy^{2}}{9za} by \frac{\left(3z^{4}a\right)^{-2}}{\left(2x^{2}y\right)^{-2}} by multiplying \frac{4xy^{2}}{9za} by the reciprocal of \frac{\left(3z^{4}a\right)^{-2}}{\left(2x^{2}y\right)^{-2}}.

$$\frac{4xy^{2}\times \left(2x^{2}y\right)^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Expand \left(2x^{2}y\right)^{-2}.

$$\frac{4xy^{2}\times 2^{-2}\left(x^{2}\right)^{-2}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{4xy^{2}\times 2^{-2}x^{-4}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{4xy^{2}\times \frac{1}{4}x^{-4}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Multiply 4 and \frac{1}{4} to get 1.

$$\frac{xy^{2}x^{-4}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$\frac{x^{-3}y^{2}y^{-2}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Multiply y^{2} and y^{-2} to get 1.

$$\frac{x^{-3}}{9za\times \left(3z^{4}a\right)^{-2}}$$

Expand \left(3z^{4}a\right)^{-2}.

$$\frac{x^{-3}}{9za\times 3^{-2}\left(z^{4}\right)^{-2}a^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{x^{-3}}{9za\times 3^{-2}z^{-8}a^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{x^{-3}}{9za\times \frac{1}{9}z^{-8}a^{-2}}$$

Multiply 9 and \frac{1}{9} to get 1.

$$\frac{x^{-3}}{zaz^{-8}a^{-2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -8 to get -7.

$$\frac{x^{-3}}{z^{-7}aa^{-2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{x^{-3}}{z^{-7}a^{-1}}$$