Solve (a^{3}*a^4)^2div(a^3)^2diva

$$( a ^ { 3 } \cdot a ^ { 4 } ) ^ { 2 } \div ( a ^ { 3 } ) ^ { 2 } \div a$$

Evaluate

$$a^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\frac{\left(a^{7}\right)^{2}}{\left(a^{3}\right)^{2}}}{a}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\frac{a^{14}}{\left(a^{3}\right)^{2}}}{a}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\frac{a^{14}}{a^{6}}}{a}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 14 to get 8.

$$\frac{a^{8}}{a}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 8 to get 7.

$$a^{7}$$

Expand

$$a^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\frac{\left(a^{7}\right)^{2}}{\left(a^{3}\right)^{2}}}{a}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\frac{a^{14}}{\left(a^{3}\right)^{2}}}{a}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\frac{a^{14}}{a^{6}}}{a}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 14 to get 8.

$$\frac{a^{8}}{a}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 8 to get 7.

$$a^{7}$$