Solve =( a^ 4 * b^ -2 c^ 3 )^ 2 *( a^ 2 * b^ 3 c^ 2 )^ 3 epsilon | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$=(\frac{a^{4}\cdot b^{-2}}{c^{3}})^{2}\times(\frac{a^{2}\cdot b^{3}}{c^{2}})^{3}\epsilon$$

Evaluate

$\frac{ϵb^{5}a^{14}}{c^{12}}$

Solution Steps

To raise $\frac{a^{4}b^{-2}}{c^{3}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}}\times \left(\frac{a^{2}b^{3}}{c^{2}}\right)^{3}ϵ$$

To raise $\frac{a^{2}b^{3}}{c^{2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}}\times \frac{\left(a^{2}b^{3}\right)^{3}}{\left(c^{2}\right)^{3}}ϵ$$

Multiply $\frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}}$ times $\frac{\left(a^{2}b^{3}\right)^{3}}{\left(c^{2}\right)^{3}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}}{\left(c^{3}\right)^{2}\left(c^{2}\right)^{3}}ϵ$$

Express $\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}}{\left(c^{3}\right)^{2}\left(c^{2}\right)^{3}}ϵ$ as a single fraction.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{\left(c^{3}\right)^{2}\left(c^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $2$ to get $6$.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{6}\left(c^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $3$ to get $6$.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{6}c^{6}}$$

To multiply powers of the same base, add their exponents. Add $6$ and $6$ to get $12$.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

Expand $\left(a^{4}b^{-2}\right)^{2}$.

$$\frac{\left(a^{4}\right)^{2}\left(b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$\frac{a^{8}\left(b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $-2$ and $2$ to get $-4$.

$$\frac{a^{8}b^{-4}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

Expand $\left(a^{2}b^{3}\right)^{3}$.

$$\frac{a^{8}b^{-4}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $3$ to get $6$.

$$\frac{a^{8}b^{-4}a^{6}\left(b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{a^{8}b^{-4}a^{6}b^{9}ϵ}{c^{12}}$$

To multiply powers of the same base, add their exponents. Add $8$ and $6$ to get $14$.

$$\frac{a^{14}b^{-4}b^{9}ϵ}{c^{12}}$$

To multiply powers of the same base, add their exponents. Add $-4$ and $9$ to get $5$.

$$\frac{a^{14}b^{5}ϵ}{c^{12}}$$

Expand

$\frac{ϵb^{5}a^{14}}{c^{12}}$

Solution Steps

To raise $\frac{a^{4}b^{-2}}{c^{3}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}}\times \left(\frac{a^{2}b^{3}}{c^{2}}\right)^{3}ϵ$$

To raise $\frac{a^{2}b^{3}}{c^{2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}}\times \frac{\left(a^{2}b^{3}\right)^{3}}{\left(c^{2}\right)^{3}}ϵ$$

Multiply $\frac{\left(a^{4}b^{-2}\right)^{2}}{\left(c^{3}\right)^{2}}$ times $\frac{\left(a^{2}b^{3}\right)^{3}}{\left(c^{2}\right)^{3}}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}}{\left(c^{3}\right)^{2}\left(c^{2}\right)^{3}}ϵ$$

Express $\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}}{\left(c^{3}\right)^{2}\left(c^{2}\right)^{3}}ϵ$ as a single fraction.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{\left(c^{3}\right)^{2}\left(c^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $2$ to get $6$.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{6}\left(c^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $3$ to get $6$.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{6}c^{6}}$$

To multiply powers of the same base, add their exponents. Add $6$ and $6$ to get $12$.

$$\frac{\left(a^{4}b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

Expand $\left(a^{4}b^{-2}\right)^{2}$.

$$\frac{\left(a^{4}\right)^{2}\left(b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$\frac{a^{8}\left(b^{-2}\right)^{2}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $-2$ and $2$ to get $-4$.

$$\frac{a^{8}b^{-4}\left(a^{2}b^{3}\right)^{3}ϵ}{c^{12}}$$

Expand $\left(a^{2}b^{3}\right)^{3}$.

$$\frac{a^{8}b^{-4}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $3$ to get $6$.

$$\frac{a^{8}b^{-4}a^{6}\left(b^{3}\right)^{3}ϵ}{c^{12}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{a^{8}b^{-4}a^{6}b^{9}ϵ}{c^{12}}$$

To multiply powers of the same base, add their exponents. Add $8$ and $6$ to get $14$.

$$\frac{a^{14}b^{-4}b^{9}ϵ}{c^{12}}$$

To multiply powers of the same base, add their exponents. Add $-4$ and $9$ to get $5$.

$$\frac{a^{14}b^{5}ϵ}{c^{12}}$$