Pre-Algebra Examples

${(3 x^{9} y^{7})}^{- 3} (8 x^{3} y^{9})$

Step 1

Rewrite using the commutative property of multiplication.

$8 {(3 x^{9} y^{7})}^{- 3} x^{3} y^{9}$

Step 2

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

$8 \frac{1}{{(3 x^{9} y^{7})}^{3}} x^{3} y^{9}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $3 x^{9} y^{7}$ .

$8 \frac{1}{{(3 x^{9})}^{3} {(y^{7})}^{3}} x^{3} y^{9}$

Step 3.2

Apply the product rule to $3 x^{9}$ .

$8 \frac{1}{3^{3} {(x^{9})}^{3} {(y^{7})}^{3}} x^{3} y^{9}$

Step 3.3

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

$8 \frac{1}{27 {(x^{9})}^{3} {(y^{7})}^{3}} x^{3} y^{9}$

Step 3.4

Multiply the exponents in ${(x^{9})}^{3}$ .

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Step 3.4.1

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

$8 \frac{1}{27 x^{9 \cdot 3} {(y^{7})}^{3}} x^{3} y^{9}$

Step 3.4.2

Multiply $9$ by $3$ .

$8 \frac{1}{27 x^{27} {(y^{7})}^{3}} x^{3} y^{9}$

Step 3.5

Multiply the exponents in ${(y^{7})}^{3}$ .

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Step 3.5.1

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

$8 \frac{1}{27 x^{27} y^{7 \cdot 3}} x^{3} y^{9}$

Step 3.5.2

Multiply $7$ by $3$ .

$8 \frac{1}{27 x^{27} y^{21}} x^{3} y^{9}$

Step 4

Simplify terms.

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Step 4.1

Combine $8$ and $\frac{1}{27 x^{27} y^{21}}$ .

$\frac{8}{27 x^{27} y^{21}} x^{3} y^{9}$

Step 4.2

Cancel the common factor of $x^{3}$ .

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Step 4.2.1

Factor $x^{3}$ out of $27 x^{27} y^{21}$ .

$\frac{8}{x^{3} (27 x^{24} y^{21})} x^{3} y^{9}$

Step 4.2.2

Cancel the common factor.

$\frac{8}{x^{3} (27 x^{24} y^{21})} x^{3} y^{9}$

Step 4.2.3

Rewrite the expression.

$\frac{8}{27 x^{24} y^{21}} y^{9}$

Step 4.3

Cancel the common factor of $y^{9}$ .

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Step 4.3.1

Factor $y^{9}$ out of $27 x^{24} y^{21}$ .

$\frac{8}{y^{9} (27 x^{24} y^{12})} y^{9}$

Step 4.3.2

Cancel the common factor.

$\frac{8}{y^{9} (27 x^{24} y^{12})} y^{9}$

Step 4.3.3

Rewrite the expression.

$\frac{8}{27 x^{24} y^{12}}$