Solve ((3x)/(7y ^ 2)) ^ - 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

$$(\frac{3x}{7y^{2}})^{-2}.$$

Evaluate

$\frac{49y^{4}}{9x^{2}}$

Solution Steps

To raise $\frac{3x}{7y^{2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x\right)^{-2}}{\left(7y^{2}\right)^{-2}}$$

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

$$\frac{3^{-2}x^{-2}}{\left(7y^{2}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}x^{-2}}{\left(7y^{2}\right)^{-2}}$$

Expand $\left(7y^{2}\right)^{-2}$.

$$\frac{\frac{1}{9}x^{-2}}{7^{-2}\left(y^{2}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}x^{-2}}{7^{-2}y^{-4}}$$

Calculate $7$ to the power of $-2$ and get $\frac{1}{49}$.

$$\frac{\frac{1}{9}x^{-2}}{\frac{1}{49}y^{-4}}$$

Expand

$\frac{49y^{4}}{9x^{2}}$

Solution Steps

To raise $\frac{3x}{7y^{2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x\right)^{-2}}{\left(7y^{2}\right)^{-2}}$$

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

$$\frac{3^{-2}x^{-2}}{\left(7y^{2}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}x^{-2}}{\left(7y^{2}\right)^{-2}}$$

Expand $\left(7y^{2}\right)^{-2}$.

$$\frac{\frac{1}{9}x^{-2}}{7^{-2}\left(y^{2}\right)^{-2}}$$

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

$$\frac{\frac{1}{9}x^{-2}}{7^{-2}y^{-4}}$$

Calculate $7$ to the power of $-2$ and get $\frac{1}{49}$.

$$\frac{\frac{1}{9}x^{-2}}{\frac{1}{49}y^{-4}}$$