Simplify (3f^4g^-3)^3(f^2g^-2)^-1

${(3 f^{4} g^{- 3})}^{3} {(f^{2} g^{- 2})}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(3 f^{4} \frac{1}{g^{3}})}^{3} {(f^{2} g^{- 2})}^{- 1}$

Step 2

Multiply $3 f^{4} \frac{1}{g^{3}}$ .

Combine $3$ and $\frac{1}{g^{3}}$ .

${(f^{4} \frac{3}{g^{3}})}^{3} {(f^{2} g^{- 2})}^{- 1}$

Combine $f^{4}$ and $\frac{3}{g^{3}}$ .

${(\frac{f^{4} \cdot 3}{g^{3}})}^{3} {(f^{2} g^{- 2})}^{- 1}$

Step 3

Move $3$ to the left of $f^{4}$ .

${(\frac{3 \cdot f^{4}}{g^{3}})}^{3} {(f^{2} g^{- 2})}^{- 1}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{3 f^{4}}{g^{3}}$ .

$\frac{{(3 f^{4})}^{3}}{{(g^{3})}^{3}} {(f^{2} g^{- 2})}^{- 1}$

Apply the product rule to $3 f^{4}$ .

$\frac{3^{3} {(f^{4})}^{3}}{{(g^{3})}^{3}} {(f^{2} g^{- 2})}^{- 1}$

Step 5

Simplify the numerator.

Raise $3$ to the power of $3$ .

$\frac{27 {(f^{4})}^{3}}{{(g^{3})}^{3}} {(f^{2} g^{- 2})}^{- 1}$

Multiply the exponents in ${(f^{4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{27 f^{4 \cdot 3}}{{(g^{3})}^{3}} {(f^{2} g^{- 2})}^{- 1}$

Multiply $4$ by $3$ .

$\frac{27 f^{12}}{{(g^{3})}^{3}} {(f^{2} g^{- 2})}^{- 1}$

Step 6

Multiply the exponents in ${(g^{3})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{27 f^{12}}{g^{3 \cdot 3}} {(f^{2} g^{- 2})}^{- 1}$

Multiply $3$ by $3$ .

$\frac{27 f^{12}}{g^{9}} {(f^{2} g^{- 2})}^{- 1}$

Step 7

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{27 f^{12}}{g^{9}} {(f^{2} \frac{1}{g^{2}})}^{- 1}$

Step 8

Combine $f^{2}$ and $\frac{1}{g^{2}}$ .

$\frac{27 f^{12}}{g^{9}} {(\frac{f^{2}}{g^{2}})}^{- 1}$

Step 9

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{27 f^{12}}{g^{9}} \cdot \frac{g^{2}}{f^{2}}$

Step 10

Combine.

$\frac{27 f^{12} g^{2}}{g^{9} f^{2}}$

Step 11

Cancel the common factor of $f^{12}$ and $f^{2}$ .

Factor $f^{2}$ out of $27 f^{12} g^{2}$ .

$\frac{f^{2} (27 f^{10} g^{2})}{g^{9} f^{2}}$

Cancel the common factors.

Factor $f^{2}$ out of $g^{9} f^{2}$ .

$\frac{f^{2} (27 f^{10} g^{2})}{f^{2} g^{9}}$

Cancel the common factor.

$\frac{f^{2} (27 f^{10} g^{2})}{f^{2} g^{9}}$

Rewrite the expression.

$\frac{27 f^{10} g^{2}}{g^{9}}$

Step 12

Cancel the common factor of $g^{2}$ and $g^{9}$ .

Factor $g^{2}$ out of $27 f^{10} g^{2}$ .

$\frac{g^{2} (27 f^{10})}{g^{9}}$

Cancel the common factors.

Factor $g^{2}$ out of $g^{9}$ .

$\frac{g^{2} (27 f^{10})}{g^{2} g^{7}}$

Cancel the common factor.

$\frac{g^{2} (27 f^{10})}{g^{2} g^{7}}$

Rewrite the expression.

$\frac{27 f^{10}}{g^{7}}$

Simplify (3f^4g^-3)^3(f^2g^-2)^-1

Related Questions

Support LCMGCF.com by disabling your adblocker.