Solve 1.37a(2/3)^3*3^3

$$1.37 a ( \frac { 2 } { 3 } ) ^ { 3 } \cdot 3 ^ { 3 }$$

Evaluate

$$\frac{274a}{25}$$

Solution Steps

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$1.37a\times \frac{8}{27}\times 3^{3}$$

Convert decimal number 1.37 to fraction \frac{137}{100}.

$$\frac{137}{100}a\times \frac{8}{27}\times 3^{3}$$

Multiply \frac{137}{100} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{137\times 8}{100\times 27}a\times 3^{3}$$

Do the multiplications in the fraction \frac{137\times 8}{100\times 27}.

$$\frac{1096}{2700}a\times 3^{3}$$

Reduce the fraction \frac{1096}{2700} to lowest terms by extracting and canceling out 4.

$$\frac{274}{675}a\times 3^{3}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{274}{675}a\times 27$$

Express \frac{274}{675}\times 27 as a single fraction.

$$\frac{274\times 27}{675}a$$

Multiply 274 and 27 to get 7398.

$$\frac{7398}{675}a$$

Reduce the fraction \frac{7398}{675} to lowest terms by extracting and canceling out 27.

$$\frac{274}{25}a$$

Differentiate w.r.t. a

$$10.96$$

Steps Using Definition of a Derivative

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(1.37a\times \frac{8}{27}\times 3^{3})$$

Convert decimal number 1.37 to fraction \frac{137}{100}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{137}{100}a\times \frac{8}{27}\times 3^{3})$$

Multiply \frac{137}{100} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{137\times 8}{100\times 27}a\times 3^{3})$$

Do the multiplications in the fraction \frac{137\times 8}{100\times 27}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1096}{2700}a\times 3^{3})$$

Reduce the fraction \frac{1096}{2700} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{274}{675}a\times 3^{3})$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{274}{675}a\times 27)$$

Express \frac{274}{675}\times 27 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{274\times 27}{675}a)$$

Multiply 274 and 27 to get 7398.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{7398}{675}a)$$

Reduce the fraction \frac{7398}{675} to lowest terms by extracting and canceling out 27.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{274}{25}a)$$

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

$$\frac{274}{25}a^{1-1}$$

Subtract 1 from 1.

$$\frac{274}{25}a^{0}$$

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

$$\frac{274}{25}\times 1$$

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

$$\frac{274}{25}$$