Solve (3x^{-2})^{2}*(2x^3)^4div(12x^4)^2

$$( 3 x ^ { - 2 } ) ^ { 2 } \times ( 2 x ^ { 3 } ) ^ { 4 } \div ( 12 x ^ { 4 } ) ^ { 2 }$$

Evaluate

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Solution Steps

Expand \left(3x^{-2}\right)^{2}.

$$\frac{3^{2}\left(x^{-2}\right)^{2}\times \left(2x^{3}\right)^{4}}{\left(12x^{4}\right)^{2}}$$

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

$$\frac{3^{2}x^{-4}\times \left(2x^{3}\right)^{4}}{\left(12x^{4}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{-4}\times \left(2x^{3}\right)^{4}}{\left(12x^{4}\right)^{2}}$$

Expand \left(2x^{3}\right)^{4}.

$$\frac{9x^{-4}\times 2^{4}\left(x^{3}\right)^{4}}{\left(12x^{4}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{9x^{-4}\times 2^{4}x^{12}}{\left(12x^{4}\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{9x^{-4}\times 16x^{12}}{\left(12x^{4}\right)^{2}}$$

Multiply 9 and 16 to get 144.

$$\frac{144x^{-4}x^{12}}{\left(12x^{4}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add -4 and 12 to get 8.

$$\frac{144x^{8}}{\left(12x^{4}\right)^{2}}$$

Expand \left(12x^{4}\right)^{2}.

$$\frac{144x^{8}}{12^{2}\left(x^{4}\right)^{2}}$$

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

$$\frac{144x^{8}}{12^{2}x^{8}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{144x^{8}}{144x^{8}}$$

Cancel out 144x^{8} in both numerator and denominator.

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Factor

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