Solve ((S ^ 2 * T ^ - 2)/(S ^ 4 * T ^ 4)) ^ - 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(\frac{S^{2}T^{-2}}{S^{4}T^{4}})^{-2}$$

Evaluate

$S^{4}T^{12}$

Solution Steps

Cancel out $S^{2}$ in both numerator and denominator.

$$\left(\frac{T^{-2}}{S^{2}T^{4}}\right)^{-2}$$

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

$$\left(\frac{1}{S^{2}T^{6}}\right)^{-2}$$

To raise $\frac{1}{S^{2}T^{6}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(S^{2}T^{6}\right)^{-2}}$$

Calculate $1$ to the power of $-2$ and get $1$.

$$\frac{1}{\left(S^{2}T^{6}\right)^{-2}}$$

Expand $\left(S^{2}T^{6}\right)^{-2}$.

$$\frac{1}{\left(S^{2}\right)^{-2}\left(T^{6}\right)^{-2}}$$

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

$$\frac{1}{S^{-4}\left(T^{6}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply $6$ and $-2$ to get $-12$.

$$\frac{1}{S^{-4}T^{-12}}$$

Expand

$S^{4}T^{12}$

Solution Steps

Cancel out $S^{2}$ in both numerator and denominator.

$$\left(\frac{T^{-2}}{S^{2}T^{4}}\right)^{-2}$$

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

$$\left(\frac{1}{S^{2}T^{6}}\right)^{-2}$$

To raise $\frac{1}{S^{2}T^{6}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-2}}{\left(S^{2}T^{6}\right)^{-2}}$$

Calculate $1$ to the power of $-2$ and get $1$.

$$\frac{1}{\left(S^{2}T^{6}\right)^{-2}}$$

Expand $\left(S^{2}T^{6}\right)^{-2}$.

$$\frac{1}{\left(S^{2}\right)^{-2}\left(T^{6}\right)^{-2}}$$

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

$$\frac{1}{S^{-4}\left(T^{6}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply $6$ and $-2$ to get $-12$.

$$\frac{1}{S^{-4}T^{-12}}$$