Solve a^7:a^3=

$$a ^ { 7 } : a ^ { 3 } =$$

Evaluate

$$a^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{7}}{a^{3}}$$

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

$$a^{7-3}$$

Subtract 3 from 7.

$$a^{4}$$

Differentiate w.r.t. a

$$4a^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{7-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4})$$

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}.

$$4a^{4-1}$$

Do the arithmetic.

$$4a^{3}$$