Solve frac{20t^{-6}a^-3}{(4t^-3a^2)^-2}

$$\frac { 20 t ^ { - 6 } a ^ { - 3 } } { ( 4 t ^ { - 3 } a ^ { 2 } ) ^ { - 2 } }$$

Evaluate

$$\frac{320a}{t^{12}}$$

Solution Steps

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

$$\frac{20t^{-6}a^{-3}}{4^{-2}\left(t^{-3}\right)^{-2}\left(a^{2}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -2 to get 6.

$$\frac{20t^{-6}a^{-3}}{4^{-2}t^{6}\left(a^{2}\right)^{-2}}$$

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

$$\frac{20t^{-6}a^{-3}}{4^{-2}t^{6}a^{-4}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{20t^{-6}a^{-3}}{\frac{1}{16}t^{6}a^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{20t^{-6}a^{1}}{\frac{1}{16}t^{6}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{20a^{1}}{\frac{1}{16}t^{12}}$$

Calculate a to the power of 1 and get a.

$$\frac{20a}{\frac{1}{16}t^{12}}$$

Expand

$$\frac{320a}{t^{12}}$$

Solution Steps

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

$$\frac{20t^{-6}a^{-3}}{4^{-2}\left(t^{-3}\right)^{-2}\left(a^{2}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and -2 to get 6.

$$\frac{20t^{-6}a^{-3}}{4^{-2}t^{6}\left(a^{2}\right)^{-2}}$$

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

$$\frac{20t^{-6}a^{-3}}{4^{-2}t^{6}a^{-4}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{20t^{-6}a^{-3}}{\frac{1}{16}t^{6}a^{-4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{20t^{-6}a^{1}}{\frac{1}{16}t^{6}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{20a^{1}}{\frac{1}{16}t^{12}}$$

Calculate a to the power of 1 and get a.

$$\frac{20a}{\frac{1}{16}t^{12}}$$