Solve 2b-5|(-7)^11div(-7)^4

$$2 b - 5 | ( - 7 ) ^ { 11 } \div ( - 7 ) ^ { 4 }$$

Evaluate

$$2b-4117715$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 11 to get 7.

$$2b-5|\left(-7\right)^{7}|$$

Calculate -7 to the power of 7 and get -823543.

$$2b-5|-823543|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -823543 is 823543.

$$2b-5\times 823543$$

Multiply 5 and 823543 to get 4117715.

$$2b-4117715$$

Differentiate w.r.t. b

$$2$$

Steps Using Derivative Rule for Sum

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 11 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b-5|\left(-7\right)^{7}|)$$

Calculate -7 to the power of 7 and get -823543.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b-5|-823543|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -823543 is 823543.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b-5\times 823543)$$

Multiply 5 and 823543 to get 4117715.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b-4117715)$$

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}.

$$2b^{1-1}$$

Subtract 1 from 1.

$$2b^{0}$$

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

$$2\times 1$$

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

$$2$$