Solve ( 1/2 a^(2)c^(5))^(4)/( 1/4 a^(4)c^(9))^(2)

Question

Simplify the expression

c^{2}

Evaluate

\frac{( \frac{1}{2} a ^{2} c ^{5} ) ^{4}}{( \frac{1}{4} a ^{4} c ^{9} ) ^{2}}

Evaluate the power

More Steps

Evaluate

(\frac{1}{2} a^{2} c^{5})^{4}

To raise a product to a power,raise each factor to that power

(\frac{1}{2})^{4} (a^{2})^{4} (c^{5})^{4}

Evaluate the power

More Steps

Evaluate

(\frac{1}{2})^{4}

To raise a fraction to a power,raise the numerator and denominator to that power

\frac{1 ^{4}}{2 ^{4}}

Evaluate the power

\frac{1}{2 ^{4}}

Evaluate the power

\frac{1}{16}

\frac{1}{16} (a^{2})^{4} (c^{5})^{4}

Evaluate the power

More Steps

Evaluate

(a^{2})^{4}

Multiply the exponents

a^{2 \times 4}

Multiply the terms

a^{8}

\frac{1}{16} a^{8} (c^{5})^{4}

Evaluate the power

More Steps

Evaluate

(c^{5})^{4}

Multiply the exponents

c^{5 \times 4}

Multiply the terms

c^{20}

\frac{1}{16} a^{8} c^{20}

\frac{\frac{1}{16} a ^{8} c ^{20}}{( \frac{1}{4} a ^{4} c ^{9} ) ^{2}}

Evaluate the power

More Steps

Evaluate

(\frac{1}{4} a^{4} c^{9})^{2}

To raise a product to a power,raise each factor to that power

(\frac{1}{4})^{2} (a^{4})^{2} (c^{9})^{2}

Evaluate the power

More Steps

Evaluate

(\frac{1}{4})^{2}

To raise a fraction to a power,raise the numerator and denominator to that power

\frac{1 ^{2}}{4 ^{2}}

Evaluate the power

\frac{1}{4 ^{2}}

Evaluate the power

\frac{1}{16}

\frac{1}{16} (a^{4})^{2} (c^{9})^{2}

Evaluate the power

More Steps

Evaluate

(a^{4})^{2}

Multiply the exponents

a^{4 \times 2}

Multiply the terms

a^{8}

\frac{1}{16} a^{8} (c^{9})^{2}

Evaluate the power

More Steps

Evaluate

(c^{9})^{2}

Multiply the exponents

c^{9 \times 2}

Multiply the terms

c^{18}

\frac{1}{16} a^{8} c^{18}

\frac{\frac{1}{16} a ^{8} c ^{20}}{\frac{1}{16} a ^{8} c ^{18}}

Rewrite the expression

\frac{\frac{a ^{8} c ^{20}}{16}}{\frac{1}{16} a ^{8} c ^{18}}

Rewrite the expression

\frac{\frac{a ^{8} c ^{20}}{16}}{\frac{a ^{8} c ^{18}}{16}}

Multiply by the reciprocal

\frac{a ^{8} c ^{20}}{16} \times \frac{16}{a ^{8} c ^{18}}

Cancel out the common factor a^{8}

\frac{c ^{20}}{16} \times \frac{16}{c ^{18}}

Cancel out the common factor c^{18}

\frac{c ^{2}}{16} \times 16

Cancel out the common factor 16

c^{2} \times 1

Solution

c^{2}

Show Solution

Find the excluded values

a = 0, c = 0

Evaluate

\frac{( \frac{1}{2} a ^{2} c ^{5} ) ^{4}}{( \frac{1}{4} a ^{4} c ^{9} ) ^{2}}

To find the excluded values,set the denominators equal to 0

(\frac{1}{4} a^{4} c^{9})^{2} = 0

Evaluate the power

More Steps

Evaluate

(\frac{1}{4} a^{4} c^{9})^{2}

To raise a product to a power,raise each factor to that power

(\frac{1}{4})^{2} (a^{4})^{2} (c^{9})^{2}

Evaluate the power

More Steps

Evaluate

(\frac{1}{4})^{2}

To raise a fraction to a power,raise the numerator and denominator to that power

\frac{1 ^{2}}{4 ^{2}}

Evaluate the power

\frac{1}{4 ^{2}}

Evaluate the power

\frac{1}{16}

\frac{1}{16} (a^{4})^{2} (c^{9})^{2}

Evaluate the power

More Steps

Evaluate

(a^{4})^{2}

Multiply the exponents

a^{4 \times 2}

Multiply the terms

a^{8}

\frac{1}{16} a^{8} (c^{9})^{2}

Evaluate the power

More Steps

Evaluate

(c^{9})^{2}

Multiply the exponents

c^{9 \times 2}

Multiply the terms

c^{18}

\frac{1}{16} a^{8} c^{18}

\frac{1}{16} a^{8} c^{18} = 0

Evaluate

a^{8} c^{18} = 0

Separate the equation into 2 possible cases

a^{8} = 0 c^{18} = 0

The only way a power can be 0 is when the base equals 0

a = 0 c^{18} = 0

The only way a power can be 0 is when the base equals 0

a = 0 c = 0

Solution

a = 0, c = 0

Show Solution