Solve a^4*a^8*a^4diva^3=

$$a ^ { 4 } \cdot a ^ { 8 } \cdot a ^ { 4 } \div a ^ { 3 } =$$

Evaluate

$$a^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{a^{12}a^{4}}{a^{3}}$$

To multiply powers of the same base, add their exponents. Add 12 and 4 to get 16.

$$\frac{a^{16}}{a^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 16 to get 13.

$$a^{13}$$

Differentiate w.r.t. a

$$13a^{12}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{4}a^{8}}{1}a^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{12}a^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$a^{12}a^{1-1}$$

Do the arithmetic.

$$a^{12}a^{0}$$

For any term t except 0, t^{0}=1.

$$a^{12}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$a^{12}$$