Pre-Algebra Examples

$9^{8} \div 3^{2} x \cdot 3^{- 6} \div 2^{3} + 2^{0}$

Step 1

Rewrite the division as a fraction.

$\frac{9^{8} \div 3^{2} x \cdot 3^{- 6}}{2^{3}} + 2^{0}$

Step 2

Move $3^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{9^{8} \div 3^{2} x}{2^{3} \cdot 3^{6}} + 2^{0}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$9^{8} \div 3^{2} x \cdot \frac{1}{2^{3} \cdot 3^{6}} + 2^{0}$

Step 4

Combine.

$\frac{9^{8} \cdot 1}{3^{2} x (2^{3} \cdot 3^{6})} + 2^{0}$

Step 5

Multiply $3^{2}$ by $3^{6}$ by adding the exponents.

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Step 5.1

Move $3^{6}$ .

$\frac{9^{8} \cdot 1}{3^{6} \cdot 3^{2} x \cdot 2^{3}} + 2^{0}$

Step 5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9^{8} \cdot 1}{3^{6 + 2} x \cdot 2^{3}} + 2^{0}$

Step 5.3

Add $6$ and $2$ .

$\frac{9^{8} \cdot 1}{3^{8} x \cdot 2^{3}} + 2^{0}$

Step 6

Multiply $9^{8}$ by $1$ .

$\frac{9^{8}}{3^{8} x \cdot 2^{3}} + 2^{0}$

Step 7

Raise $9$ to the power of $8$ .

$\frac{43046721}{3^{8} x \cdot 2^{3}} + 2^{0}$

Step 8

Simplify the denominator.

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Step 8.1

Raise $3$ to the power of $8$ .

$\frac{43046721}{6561 x \cdot 2^{3}} + 2^{0}$

Step 8.2

Raise $2$ to the power of $3$ .

$\frac{43046721}{6561 x \cdot 8} + 2^{0}$

Step 8.3

Multiply $8$ by $6561$ .

$\frac{43046721}{52488 x} + 2^{0}$

Step 9

Cancel the common factor of $43046721$ and $52488$ .

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Step 9.1

Factor $6561$ out of $43046721$ .

$\frac{6561 (6561)}{52488 x} + 2^{0}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $6561$ out of $52488 x$ .

$\frac{6561 (6561)}{6561 (8 x)} + 2^{0}$

Step 9.2.2

Cancel the common factor.

$\frac{6561 \cdot 6561}{6561 (8 x)} + 2^{0}$

Step 9.2.3

Rewrite the expression.

$\frac{6561}{8 x} + 2^{0}$

Step 10

Anything raised to $0$ is $1$ .

$\frac{6561}{8 x} + 1$