Solve -9^4x-9^7/3^43^3/{left(frac{1{3}right)}^-7}

$$\frac{ \frac{ { -9 }^{ 4 } x { -9 }^{ 7 } }{ { 3 }^{ 4 } } { 3 }^{ 3 } }{ { \left( \frac{ 1 }{ 3 } \right) }^{ -7 } }$$

Evaluate

$$-4782969x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\frac{\left(-9\right)^{11}x}{3^{4}}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate -9 to the power of 11 and get -31381059609.

$$\frac{\frac{-31381059609x}{3^{4}}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\frac{-31381059609x}{81}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Divide -31381059609x by 81 to get -387420489x.

$$\frac{-387420489x\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-387420489x\times 27}{\left(\frac{1}{3}\right)^{-7}}$$

Multiply -387420489 and 27 to get -10460353203.

$$\frac{-10460353203x}{\left(\frac{1}{3}\right)^{-7}}$$

Calculate \frac{1}{3} to the power of -7 and get 2187.

$$\frac{-10460353203x}{2187}$$

Divide -10460353203x by 2187 to get -4782969x.

$$-4782969x$$

Differentiate w.r.t. x

$$-4782969$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{\left(-9\right)^{11}x}{3^{4}}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}})$$

Calculate -9 to the power of 11 and get -31381059609.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{-31381059609x}{3^{4}}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}})$$

Calculate 3 to the power of 4 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{-31381059609x}{81}\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}})$$

Divide -31381059609x by 81 to get -387420489x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-387420489x\times 3^{3}}{\left(\frac{1}{3}\right)^{-7}})$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-387420489x\times 27}{\left(\frac{1}{3}\right)^{-7}})$$

Multiply -387420489 and 27 to get -10460353203.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-10460353203x}{\left(\frac{1}{3}\right)^{-7}})$$

Calculate \frac{1}{3} to the power of -7 and get 2187.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-10460353203x}{2187})$$

Divide -10460353203x by 2187 to get -4782969x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4782969x)$$

The derivative of ax^{n} is nax^{n-1}.

$$-4782969x^{1-1}$$

Subtract 1 from 1.

$$-4782969x^{0}$$

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

$$-4782969$$