Evaluate ((7/9)^-3*(3/7)^5)÷((3/7)^6)

${(\frac{7}{9})}^{- 3} \cdot {(\frac{3}{7})}^{5} \div {(\frac{3}{7})}^{6}$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{7}{9})}^{- 3} \cdot {(\frac{3}{7})}^{5}}{{(\frac{3}{7})}^{6}}$

Step 2

Simplify terms.

Move ${(\frac{7}{9})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(\frac{3}{7})}^{5}}{{(\frac{3}{7})}^{6} {(\frac{7}{9})}^{3}}$

Cancel the common factor of ${(\frac{3}{7})}^{5}$ and ${(\frac{3}{7})}^{6}$ .

Multiply by $1$ .

$\frac{{(\frac{3}{7})}^{5} \cdot 1}{{(\frac{3}{7})}^{6} {(\frac{7}{9})}^{3}}$

Cancel the common factors.

Factor ${(\frac{3}{7})}^{5}$ out of ${(\frac{3}{7})}^{6} {(\frac{7}{9})}^{3}$ .

$\frac{{(\frac{3}{7})}^{5} \cdot 1}{{(\frac{3}{7})}^{5} (\frac{3}{7} {(\frac{7}{9})}^{3})}$

Cancel the common factor.

$\frac{{(\frac{3}{7})}^{5} \cdot 1}{{(\frac{3}{7})}^{5} (\frac{3}{7} {(\frac{7}{9})}^{3})}$

Rewrite the expression.

$\frac{1}{\frac{3}{7} {(\frac{7}{9})}^{3}}$

Combine $\frac{3}{7}$ and ${(\frac{7}{9})}^{3}$ .

$\frac{1}{\frac{3 {(\frac{7}{9})}^{3}}{7}}$

Step 3

Simplify the numerator.

Apply the product rule to $\frac{7}{9}$ .

$\frac{1}{\frac{3 \frac{7^{3}}{9^{3}}}{7}}$

Raise $7$ to the power of $3$ .

$\frac{1}{\frac{3 \frac{343}{9^{3}}}{7}}$

Raise $9$ to the power of $3$ .

$\frac{1}{\frac{3 (\frac{343}{729})}{7}}$

Step 4

Simplify terms.

Combine $3$ and $\frac{343}{729}$ .

$\frac{1}{\frac{\frac{3 \cdot 343}{729}}{7}}$

Multiply $3$ by $343$ .

$\frac{1}{\frac{\frac{1029}{729}}{7}}$

Cancel the common factor of $1029$ and $729$ .

Factor $3$ out of $1029$ .

$\frac{1}{\frac{\frac{3 (343)}{729}}{7}}$

Cancel the common factors.

Factor $3$ out of $729$ .

$\frac{1}{\frac{\frac{3 \cdot 343}{3 \cdot 243}}{7}}$

Cancel the common factor.

$\frac{1}{\frac{\frac{3 \cdot 343}{3 \cdot 243}}{7}}$

Rewrite the expression.

$\frac{1}{\frac{\frac{343}{243}}{7}}$

Step 5

Simplify the denominator.

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\frac{343}{243} \cdot \frac{1}{7}}$

Cancel the common factor of $7$ .

Factor $7$ out of $343$ .

$\frac{1}{\frac{7 (49)}{243} \cdot \frac{1}{7}}$

Cancel the common factor.

$\frac{1}{\frac{7 \cdot 49}{243} \cdot \frac{1}{7}}$

Rewrite the expression.

$\frac{1}{\frac{49}{243}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{243}{49})$

Step 7

Multiply $\frac{243}{49}$ by $1$ .

$\frac{243}{49}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{243}{49}$

Decimal Form:

$4.95918367 \dots$

Mixed Number Form:

$4 \frac{47}{49}$

Evaluate ((7/9)^-3*(3/7)^5)÷((3/7)^6)

Related Questions