Solve (7x^-1)^2*(49^-2xy)^3

$$( 7 x ^ { - 1 } ) ^ { 2 } \times ( 49 ^ { - 2 } x y ) ^ { 3 }$$

Evaluate

$$\frac{xy^{3}}{282475249}$$

Solution Steps

Expand \left(7x^{-1}\right)^{2}.

$$7^{2}\left(x^{-1}\right)^{2}\times \left(49^{-2}xy\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$7^{2}x^{-2}\times \left(49^{-2}xy\right)^{3}$$

Calculate 7 to the power of 2 and get 49.

$$49x^{-2}\times \left(49^{-2}xy\right)^{3}$$

Calculate 49 to the power of -2 and get \frac{1}{2401}.

$$49x^{-2}\times \left(\frac{1}{2401}xy\right)^{3}$$

Expand \left(\frac{1}{2401}xy\right)^{3}.

$$49x^{-2}\times \left(\frac{1}{2401}\right)^{3}x^{3}y^{3}$$

Calculate \frac{1}{2401} to the power of 3 and get \frac{1}{13841287201}.

$$49x^{-2}\times \frac{1}{13841287201}x^{3}y^{3}$$

Multiply 49 and \frac{1}{13841287201} to get \frac{1}{282475249}.

$$\frac{1}{282475249}x^{-2}x^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{1}{282475249}x^{1}y^{3}$$

Calculate x to the power of 1 and get x.

$$\frac{1}{282475249}xy^{3}$$

Expand

$$\frac{xy^{3}}{282475249}$$

Solution Steps

Expand \left(7x^{-1}\right)^{2}.

$$7^{2}\left(x^{-1}\right)^{2}\times \left(49^{-2}xy\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$7^{2}x^{-2}\times \left(49^{-2}xy\right)^{3}$$

Calculate 7 to the power of 2 and get 49.

$$49x^{-2}\times \left(49^{-2}xy\right)^{3}$$

Calculate 49 to the power of -2 and get \frac{1}{2401}.

$$49x^{-2}\times \left(\frac{1}{2401}xy\right)^{3}$$

Expand \left(\frac{1}{2401}xy\right)^{3}.

$$49x^{-2}\times \left(\frac{1}{2401}\right)^{3}x^{3}y^{3}$$

Calculate \frac{1}{2401} to the power of 3 and get \frac{1}{13841287201}.

$$49x^{-2}\times \frac{1}{13841287201}x^{3}y^{3}$$

Multiply 49 and \frac{1}{13841287201} to get \frac{1}{282475249}.

$$\frac{1}{282475249}x^{-2}x^{3}y^{3}$$

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

$$\frac{1}{282475249}x^{1}y^{3}$$

Calculate x to the power of 1 and get x.

$$\frac{1}{282475249}xy^{3}$$