Solve (x^7:x^3)^9x^4=

$$( x ^ { 7 } : x ^ { 3 } ) ^ { 9 } x ^ { 4 } =$$

Evaluate

$$x^{40}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 7 to get 4.

$$\left(x^{4}\right)^{9}x^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 9 to get 36.

$$x^{36}x^{4}$$

To multiply powers of the same base, add their exponents. Add 36 and 4 to get 40.

$$x^{40}$$

Expand

$$x^{40}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 7 to get 4.

$$\left(x^{4}\right)^{9}x^{4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 9 to get 36.

$$x^{36}x^{4}$$

To multiply powers of the same base, add their exponents. Add 36 and 4 to get 40.

$$x^{40}$$