Solve (8x^{2}y^{2})^{5}:(8x^{2}y^2)^4(8x^2y^2)

$$( 8 x ^ { 2 } y ^ { 2 } ) ^ { 5 } : ( 8 x ^ { 2 } y ^ { 2 } ) ^ { 4 } ( 8 x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$64\left(xy\right)^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\left(8x^{2}y^{2}\right)^{1}\times 8x^{2}y^{2}$$

Calculate 8x^{2}y^{2} to the power of 1 and get 8x^{2}y^{2}.

$$8x^{2}y^{2}\times 8x^{2}y^{2}$$

Multiply 8 and 8 to get 64.

$$64x^{2}y^{2}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$64x^{4}y^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$64x^{4}y^{4}$$

Expand

$$64\left(xy\right)^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\left(8x^{2}y^{2}\right)^{1}\times 8x^{2}y^{2}$$

Calculate 8x^{2}y^{2} to the power of 1 and get 8x^{2}y^{2}.

$$8x^{2}y^{2}\times 8x^{2}y^{2}$$

Multiply 8 and 8 to get 64.

$$64x^{2}y^{2}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$64x^{4}y^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$64x^{4}y^{4}$$