Solve ((8 ^ 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

$$(\frac{8^{2}T^{-2}}{S^{4}T^{4}})^{-2}$$

Evaluate

$\frac{S^{8}T^{12}}{4096}$

Solution Steps

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

$$\left(\frac{8^{2}}{S^{4}T^{6}}\right)^{-2}$$

Calculate $8$ to the power of $2$ and get $64$.

$$\left(\frac{64}{S^{4}T^{6}}\right)^{-2}$$

To raise $\frac{64}{S^{4}T^{6}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{64^{-2}}{\left(S^{4}T^{6}\right)^{-2}}$$

Calculate $64$ to the power of $-2$ and get $\frac{1}{4096}$.

$$\frac{\frac{1}{4096}}{\left(S^{4}T^{6}\right)^{-2}}$$

Expand $\left(S^{4}T^{6}\right)^{-2}$.

$$\frac{\frac{1}{4096}}{\left(S^{4}\right)^{-2}\left(T^{6}\right)^{-2}}$$

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

$$\frac{\frac{1}{4096}}{S^{-8}\left(T^{6}\right)^{-2}}$$

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

$$\frac{\frac{1}{4096}}{S^{-8}T^{-12}}$$

Express $\frac{\frac{1}{4096}}{S^{-8}T^{-12}}$ as a single fraction.

$$\frac{1}{4096S^{-8}T^{-12}}$$

Expand

$\frac{S^{8}T^{12}}{4096}$

Solution Steps

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

$$\left(\frac{8^{2}}{S^{4}T^{6}}\right)^{-2}$$

Calculate $8$ to the power of $2$ and get $64$.

$$\left(\frac{64}{S^{4}T^{6}}\right)^{-2}$$

To raise $\frac{64}{S^{4}T^{6}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{64^{-2}}{\left(S^{4}T^{6}\right)^{-2}}$$

Calculate $64$ to the power of $-2$ and get $\frac{1}{4096}$.

$$\frac{\frac{1}{4096}}{\left(S^{4}T^{6}\right)^{-2}}$$

Expand $\left(S^{4}T^{6}\right)^{-2}$.

$$\frac{\frac{1}{4096}}{\left(S^{4}\right)^{-2}\left(T^{6}\right)^{-2}}$$

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

$$\frac{\frac{1}{4096}}{S^{-8}\left(T^{6}\right)^{-2}}$$

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

$$\frac{\frac{1}{4096}}{S^{-8}T^{-12}}$$

Express $\frac{\frac{1}{4096}}{S^{-8}T^{-12}}$ as a single fraction.

$$\frac{1}{4096S^{-8}T^{-12}}$$