Solve 5x(2*a^3*a^2)^4=2^4

$$5 x ( 2 \cdot a ^ { 3 } \cdot a ^ { 2 } ) ^ { 4 } = 2 ^ { 4 }$$

Solve for x

$$x=\frac{1}{5a^{20}}$$

$$a\neq 0$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$5x\times \left(2a^{5}\right)^{4}=2^{4}$$

Expand \left(2a^{5}\right)^{4}.

$$5x\times 2^{4}\left(a^{5}\right)^{4}=2^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$5x\times 2^{4}a^{20}=2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$5x\times 16a^{20}=2^{4}$$

Multiply 5 and 16 to get 80.

$$80xa^{20}=2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$80xa^{20}=16$$

The equation is in standard form.

$$80a^{20}x=16$$

Divide both sides by 80a^{20}.

$$\frac{80a^{20}x}{80a^{20}}=\frac{16}{80a^{20}}$$

Dividing by 80a^{20} undoes the multiplication by 80a^{20}.

$$x=\frac{16}{80a^{20}}$$

Divide 16 by 80a^{20}.

$$x=\frac{1}{5a^{20}}$$

Solve for a

$$a=\frac{5^{\frac{19}{20}}}{5\sqrt[20]{x}}$$

$$a=-\frac{5^{\frac{19}{20}}}{5\sqrt[20]{x}}\text{, }x>0$$